Yes, the S1 can output 4K 60p (in aps-c crop) 10-bit 4:2:2 to an HDMI recorder.
The S1 has some nice features when paired with the native Lumix 24-105 lens, but it has some drawbacks too, particularly on a gimbal.
The native lenses are pretty expensive and pretty big and heavy. I use the S1 and 24-105 f/4 on my Weebill S and it is a bit hard for me to keep under control.
The 24-105 is so big that you have to slide the whole rig back real far on the weebill s and that can limit how far up you can tilt the screen (I tend to shoot close to waist level on a gimbal, so it might be less of a bother to others who hold the camera closer to eye level).
Oh, and that is with the 24-105 at the 24mm end. If you zoom in, then the barrel extends a LOT and you will have to rebalance and move the camera further back on the gimbal, if that is even possible.
The S1 has two zebra memory positions, but unlike the S1H, you can't show BOTH zebras at the same time.
On the other hand, some good things are that:
The 25-105 is about as parfocal as can be, as far as I can tell and have seen on the internets
The 24-105 has minimal focus breathing.
While we all know about Panasonic DFD autofcus, doing a focus pull using the touch screen is REALLY smooth. It isn't fast, but it very gently eases in to the new focus point. It probably eases out from the first focus point, too. Yes, it is far slower than my Sony cameras, but it is much, much smoother and is pretty similar to a really good manual focus pull. (Much better than I can do manually.)
And speaking of manual focus pulls, the S1 allows you to set the 24-105 to a linear focus response when turning the focus ring (so much better than the typical focus by wire response), and...
You can adjust the amount of degrees of rotation in the focus ring from minimum focus distance to infinity. I think you can have a minimum of 90-degrees and a max of at least 360-degrees. There is a setting that says "Maximum" but got no clue what that means.
The other good news is that the Sigma MC-21 seems to work pretty well with a lot of Canon glass (at least for AF-S, there is no AF-C at this time with the SA-21 adapter and ANY lens, either sigma or canon), and your typical manual vintage FF lenses work well on the S1.
That's a good thing because there isn't a whole lot of L Mount glass available now. For example, the only native 50mm lens is an f/1.4 costs around $2,300 and there isn't anything on any lens roadmap for a native 50mm f/1.8 for a couple hundred dollars. There is an 85mm f/1.8 on Panasonic's lens roadmap, but I wouldn't be surprised if it is big, heavy and expensive.