ac6000cw

Yes (as the main audio - I'm just using it for amateur outdoor documentary stuff).
It's the 32-bit float that is the attraction, as it makes audio input level adjustment on the recorder something else I don't have to worry about. Same reason I normally use shutter-priority auto exposure for video - it leaves me free to concentrate on framing and holding the camera still (or moving it smoothly).
Yes - I want stereo ambient sound but the VP83F is mono super-cardioid (and somewhat larger in size).
I prefer a 90 degree X-Y cardioid stereo configuration, as that gives me the sound-stage width I prefer. I often use a Tascam TM2X stereo on-camera mic (without the extension arm!) as the size versus quality balance of that works for me. I've tried others over the years (both mics and recorders) but that's the one I keep coming back to.
What would be really nice is a mirrorless ILC camera with 32-bit float audio support...

I've owned both (and the E-M1 iii, G80 and G9).
1. E-M1 ii is larger & heavier but has (for me) superb ergonomics and build quality. It's just a really nice camera to use.
2. E-M1 ii sound via the internal mics is way better than the GX85. It also has a mic input and headphone jack.
3. E-M1 ii 4k UHD is full sensor width (no crop) whereas the GX85 is cropped.
4. E-M1 ii has great battery life.
5. E-M1 ii IBIS is better than the GX85.
If you are seriously considering the E-M1 ii and video C-AF and IBIS are important to you, think about the E-M1 iii instead if you can afford it - it has better video C-AF and a choice of IBIS settings (the +1 setting is almost tripod-level).
Another cheap (used) alternative to the GX85 worth considering is the G80/G85 - same sensor in a larger body with better IBIS, larger battery and a mic input.
Provided the size is OK for you, the G9 is superb value used, and easily beats any of the above cameras for video quality (it also supports 10-bit video and 4k 60p, which none of the others do). Here in the UK, the E-M1 ii and G9 cost about the same used.

In reality - neither, because having played around with an S5 ii, I don't like the ergonomics of that body design, it just feels uncomfortable/awkward to use in my hand.
Ignoring that, probably the G9 ii due to smaller & lighter long telephoto lenses, probably better IBIS, lower rolling shutter and less moire issues (assuming the video performance is comparable to a GH6).

I think a small proportion of camera owners are just generally skittish/followers of fashion, whereas most users buy a camera and only consider changing it when it breaks or no longer meets their requirements (which could be for performance/size/weight/fashion reasons among others).
Based on what I've seen at camera store 'open days' and exhibitions, Olympus/OMDS does have good brand loyalty but it's a bit of a niche user base of outdoors types (especially wildlife photographers) and those who like small/light cameras. I've never felt that Lumix has that sort of brand loyalty (other than in the 'more serious' video niche market maybe) - it's the 'high on features at reasonable prices' area that Panasonic has historically appeared to be targeting.
I'm probably about to become primarily an Olympus/OMDS camera user, after being basically a Panasonic 'hybrid' camera user for years (starting with a TZ7/ZS3 compact 15 years ago). It's mostly because I like the ergonomics of the E-M1 iii and OM-1 better than those of the G9 - even though that has better video quality. Not something I'd ever thought might happen a few years ago...
(The difficult decision is - do I keep the GX80? My G80 is already basically redundant. If both go then my only Panasonic camera will be the G9. Also, do I replace both GX80 & G80 with an OM-5 to keep a relatively small/light m43 body?)

My experience with non-OEM camera batteries (from a variety of 'brands') versus OEM ones is:
1. Their usable/useful capacity is usually lower (by maybe 10-20%), irrespective of their nominal capacity as stated by the supplier.
2. The battery indicator accuracy (on the camera screen) is lower.
3. They have higher self-discharge rates (i.e. when they're charged but not being used).
4. Their useful life (number of charge/discharge cycles and age) is lower.
5. The capacity versus cost is way better, so you can buy two or three of them for the cost of one OEM battery.
Beyond the OEM battery included with a camera, I've nearly always bought 'mid-price range' non-OEM batteries (and usually I have three batteries per camera) as they are so much cheaper and I'm not using them day in, day out (or earning a living from them). If I was using them hard I'd buy OEM batteries, other than maybe having a couple of non-OEM ones as an emergency backup.
If I wanted good non-OEM batteries at a reasonable price, I'd probably go for suppliers with a decent reputation in the market to protect and that you might get some after-sales support from e.g. Small Rig, Neewer, Wasabi, Hahnel etc.

I've owned both cameras (GX80 and E-M5 iii) for 2 years each. If you compare the image and audio only, I feel the GX80 has a slightly better image more often than the E-M5iii, but the audio is no comparison. The GX80 has usable audio until you film the same thing with the E-M5iii as you cannot hear the ibis working in it. On the GX80, you hear the ibis and focus motors if you have them going. Still, both have better audio than the GX850. Also, the continuous AF performance is night and day with the GX80 with the E-M5iii outperforming it in every aspect. The EVFs are also light years apart- way better on the E-M5iii. The GX80 does feel chunkier though, but no weather sealing.

I love Panasonic cameras, but I have a cold shard of hatred in my heart for whoever thought up the idea of releasing a camera as capable as the GX80 with terrible internal audio and no mic input.

I've not owned/used an E-M5 iii (played with one a few times), but I have owned the very close relative E-M1 ii, so this is based on using that camera and what I know about the E-M5 iii.
Gains:
MIc input (and better sound from the on-board mics). Better IBIS. No-crop 4k at 25 & 30p plus (excellent) C4K at 24fps (only). Good (IPX1 rated) weather-sealing. OLED viewfinder. All-I 200 Mbps compression option for FHD, otherwise it's max 50 Mbps IPB for FHD, 100 Mbps for 4k and 237 Mbps for C4K (all VBR). Simple/quick switching between stills and movie mode via the 'function lever' on the back. More physical buttons and dials, including a front function button. Lots of control programmability. The 'Super Control Panel' (Oly's equivalent of the Quick Menu) is nice/very useful.
Losses:
It's basically a plastic body (to keep the weight down - it's slightly lighter than the GX85), so maybe doesn't have the more premium feel of the GX85. The FHD video is soft. The video compression isn't as good as Panasonic at similar bitrates. Weak tripod mount. Restricted choice of focus areas in video (compared to stills). The Olympus menu system...(but you get used to it eventually). You can't save several custom video setups (only custom stills setups). If you press the video record button in a 'stills' mode it always uses P mode (irrespective of the current stills settings).
Flip-out screen on E-M5 iii versus tilt on GX85 - a personal preference thing.

It's not IBIS - it has OIS in the lens (standard SteadyShot) plus optional electronic stabilization (active SteadyShot, with a crop). It's very good in 'active' mode, but it's not up with the best stabilization from Oly/OMDS/Panasonic.

I've not owned/used an E-M5 iii (played with one a few times), but I have owned the very close relative E-M1 ii, so this is based on using that camera and what I know about the E-M5 iii.
Gains:
MIc input (and better sound from the on-board mics). Better IBIS. No-crop 4k at 25 & 30p plus (excellent) C4K at 24fps (only). Good (IPX1 rated) weather-sealing. OLED viewfinder. All-I 200 Mbps compression option for FHD, otherwise it's max 50 Mbps IPB for FHD, 100 Mbps for 4k and 237 Mbps for C4K (all VBR). Simple/quick switching between stills and movie mode via the 'function lever' on the back. More physical buttons and dials, including a front function button. Lots of control programmability. The 'Super Control Panel' (Oly's equivalent of the Quick Menu) is nice/very useful.
Losses:
It's basically a plastic body (to keep the weight down - it's slightly lighter than the GX85), so maybe doesn't have the more premium feel of the GX85. The FHD video is soft. The video compression isn't as good as Panasonic at similar bitrates. Weak tripod mount. Restricted choice of focus areas in video (compared to stills). The Olympus menu system...(but you get used to it eventually). You can't save several custom video setups (only custom stills setups). If you press the video record button in a 'stills' mode it always uses P mode (irrespective of the current stills settings).
Flip-out screen on E-M5 iii versus tilt on GX85 - a personal preference thing.

Gotta say the ZV-1 is ticking a lot of boxes.

That scenario underpinned the storyline of the excellent 1988 film 'Working Girl', directed by Mike Nichols (of 'The Graduate' fame). One of my favourite movies.
I thought that too 🙂
I think that was said (unofficially) at the time, or at least hinted at. Certainly later on Panasonic implied there had been exchanges of technology and development between the consumer and professional video divisions in the GH5 era. None of which is very surprising, really.

No experience of recording to them from a camera directly, but I use a 500GB T7 (non-Shield) at home for video files, and we use several T7 Shield drives at work for daily off-site backups. Performance is good (and doesn't slow down noticeably when they being worked hard and get hotter) and so far they've been reliable, They also seem well built.

After my little deep dive into the tiniest camera I could find, it does occur to me that the cameras that killed this market segment might soon be good enough to satisfy our requirements in this space:
Action cameras and phones have had manual controls for several product generations now, and things like the BM iPhone app has better features than many MILCs (waveforms, zebras, view LUTs, false colour, etc etc etc) The limitation on action cameras has always been the fixed wide lens, however with the Insta360 Ace Pro and its 8K sensor on 16mm FOV lens, it now has the resolution to do 4K at 32mm, 3K at 43mm, 2K at 64mm Even if you ignored the crop modes on these cameras, a 100Mbps 16mm FOV cropped in post would still be 66Mbps at 24mm FOV which is better than some of the lesser cameras in this segment, and you can reframe and stabilise in post with that approach! The Insta360 RS had an interchangeable lens module, so future models might have more normal lenses or even a module with interchangeable mounts The trend for action cameras and phones is towards larger sensors, so it's not inconceivable that we'll get an MFT action camera / smartphone down the line iPhone 15 had a professional codec and professional colour space, way ahead of most cameras discussed in this thread, with better low-light and DR than some too In a sense these will be good outcomes for us, because with the death of this market segment we have been stuck with 8-bit cameras with relatively poor codecs, limited manual controls in video, and small sensors, but I think the gap is probably about to be filled.
My vision of making super-8 style vignette videos just for fun is almost possible with the latest GoPro, because I could crop in post, grading the image to be soft and having the right colour / grain / jitter / etc, and the fixed focus lens means that my in-post lens emulation has perfect-AF and is parfocal!

I'd agree with the others that you've already found the best ILC solution.
Personally I don't expect any new very compact ILCs to appear (warmed over stuff like the G100D excepted) - I think that market segment is largely catered for now by small RX100/ZV-1 size 1" sensor compacts plus larger sensor phones. I think it's not that camera manufacturers couldn't do it, more about if there would be enough customers willing to pay a high price for something like a G9 ii sensor and processing sqeezed into a sub-GX80/GX9 size body, with the inevitable limitations on recording times and battery life.
Re. IBIS - I've now sold all my older cameras without it, because I much prefer doing most shooting handheld. I don't like an obvious 'handheld' look (overused sometimes in films and TV), so like Kye I rely on IBIS plus stabilisation in post if necessary. It's mostly why I live with video quality limitations in exchange for IBIS performance on the E-M1 iii and OM-1 (the OG G9 IBIS gets close, has worse AF and better video quality - swings and roundabouts...). The ZV-1 in 'active' SteadyShot mode (OIS + EIS) is quite decent but IMHO not up to E-M1 iii/OM-1 standard - but it is pocket sized after all...
 

I'd agree with the others that you've already found the best ILC solution.
Personally I don't expect any new very compact ILCs to appear (warmed over stuff like the G100D excepted) - I think that market segment is largely catered for now by small RX100/ZV-1 size 1" sensor compacts plus larger sensor phones. I think it's not that camera manufacturers couldn't do it, more about if there would be enough customers willing to pay a high price for something like a G9 ii sensor and processing sqeezed into a sub-GX80/GX9 size body, with the inevitable limitations on recording times and battery life.
Re. IBIS - I've now sold all my older cameras without it, because I much prefer doing most shooting handheld. I don't like an obvious 'handheld' look (overused sometimes in films and TV), so like Kye I rely on IBIS plus stabilisation in post if necessary. It's mostly why I live with video quality limitations in exchange for IBIS performance on the E-M1 iii and OM-1 (the OG G9 IBIS gets close, has worse AF and better video quality - swings and roundabouts...). The ZV-1 in 'active' SteadyShot mode (OIS + EIS) is quite decent but IMHO not up to E-M1 iii/OM-1 standard - but it is pocket sized after all...
 

I've now decided to reinstate the modified SJ4000 action camera with 20-80mm FOV zoom lens into active duty, and managed to put together a rig for it and everything.
I found an old video where I compared it to the GF3 and it seems the SJ4000 potentially has a slightly more detailed image, although I suspect that the DR is a lot less and that the colours aren't as nice.
Here's the modified rig mounted on the handlebars of my electric scooter.  It's very easy to remove them and the clamp becomes a surprisingly ergonomic handle.

I had a similar pattern of handling strange issues in Resolve.  I'd encounter some strange issue, spend an hour playing with it and reading the manual etc, then find a workable solution / workaround, then go to the forums to see if anyone else was having that problem, find the thread, and then find the post I'd made previously sharing the solution that I'd just found.

I must admit that I have been very tempted to try out the ZV-1. I guess if you want to go real cheap, the F version is a possibility as well. I've had a couple RX10ii and I really like Sony's 1" sensor cameras.

I think limited 4k recording times on very small cameras is just one of the compromises you have to accept (battery life is another) - e.g. the GX800 is limited to 5 minutes in 4k, the LX100 and TZ100 to 15 minutes.
This is the recording time info in the manual for the ZV-1:

I think limited 4k recording times on very small cameras is just one of the compromises you have to accept (battery life is another) - e.g. the GX800 is limited to 5 minutes in 4k, the LX100 and TZ100 to 15 minutes.
This is the recording time info in the manual for the ZV-1:

If the LX10 is a possibility, then maybe the Sony ZV-1 (the original version)?
Lens OIS (plus EIS in 'Active' stabilization mode). Also records gyro data for stabilization in post.
4k 24/25/30p at 100Mbps, FHD at 50Mbps, no crop in 4k, Cine/S-Log/HLG picture profiles (but only 8-bit).
PDAF.
Startup time about 3 seconds, including adjusting the zoom to where it was last time.
Good on-board audio (with an included furry) plus a mic jack (which doesn't foul the screen when it's hinged out).
The manual is here - https://helpguide.sony.net/dc/1910/v1/en/index.html
Downsides that I've noticed so far:
The battery life when shooting video is poor (there's just not the space for a large battery in a body that small...but 3rd party batteries are cheap)
Anything screwed into the tripod hole blocks the battery/card door from opening.
Only one control wheel.
The Sony menus...

I own the last three lenses on that list.
The 20mm F1.7 is a nice lens optically, but for video use its AF is noisy and the minimum aperture is F16 (versus F22 for most micro4/3 lenses). No OIS.
The Pana 12-32mm F3.5-5.6 is nice - weighs almost nothing and is very compact when closed and has OIS (with dual-IS support on the GX85 etc.). No manual focus ring, which means no MF on Olympus/OMDS bodies as they don't support MF adjustment via the camera body controls (AFAIK all Olympus lenses have a focus control). Panasonic does support body MF control for it. Tends to be my go-to lens if I'm taking a second camera on a trip, to keep the size down.
Olympus M.Zuiko Digital ED 14-42mm F3.5-5.6 EZ - I think it's OK but nothing special - the power zoom isn't especially smooth, but it does have both zoom and focus rings on a slim pancake lens.

In the small/light/cheap micro4/3 lens category, the Pan 14-42mm F3.5-5.6 II kit lens is worth considering - twice the length of the 12-32mm, but has a focus ring and (on my copy at least) a smoother zoom ring. Both lenses on a GX85:

I own the last three lenses on that list.
The 20mm F1.7 is a nice lens optically, but for video use its AF is noisy and the minimum aperture is F16 (versus F22 for most micro4/3 lenses). No OIS.
The Pana 12-32mm F3.5-5.6 is nice - weighs almost nothing and is very compact when closed and has OIS (with dual-IS support on the GX85 etc.). No manual focus ring, which means no MF on Olympus/OMDS bodies as they don't support MF adjustment via the camera body controls (AFAIK all Olympus lenses have a focus control). Panasonic does support body MF control for it. Tends to be my go-to lens if I'm taking a second camera on a trip, to keep the size down.
Olympus M.Zuiko Digital ED 14-42mm F3.5-5.6 EZ - I think it's OK but nothing special - the power zoom isn't especially smooth, but it does have both zoom and focus rings on a slim pancake lens.

Here are a few old 2160p25 and 1080p50 SOC clips from my GX800 (which I no longer have) - https://drive.google.com/open?id=13vWtrMzGKQ5qR1l2zCr_NBVjIowFuy4V&usp=drive_fs .  All hand-held, probably using the 12-32mm or 14-42mm kit lenses, standard picture profile, shutter priority (using the 'flicker reduction' setting). The train going over the road crossing (P1000474.MP4) shows the rolling shutter nicely.