A change to the effective F/stop that would affect the DOF means a physical change to the size of the opening created by the shutter blades. Nowhere in the documentation does it state or even suggest that this happens.
If you were to take a picture, print it out and hold it up to your face close enough that you couldn't see its edges, that represents pre-Metabones or how your smaller-sensor camera sees the scene depicted in the photograph. Now, hold the photograph out further, far enough so that you can see all the way to the edges or close. That represents how your smaller-sensor camera sees the scene depicted in the photograph after installing the Metabones adapter.
No change in DOF. The optical reduction doesn't alter the FOV of the lens it alters how much of it your sensor can see. This isn't a wide-angle converter that also makes the image brighter. The effective T-Stop difference is from the compression of the light meant for a large aperture imaging layer into the space of a smaller one. Light is additive.
In image processing terms, when you scale an image from 2K to 1K the brightness of the image doesn't change because neighboring pixels from the 2K source are averaged to create a new pixel for the 1K result. Light doesn't work that way. Resizing would do something similar to what this adapter does if, instead of averaging, you were scoot neighboring pixels from the 2K source inward such that the 1K final still contained all of the original pixels from the 2K but some of them were now stacked on top of the other and their values were now added to each other rather than averaged.
The Metabones adapter doesn't stack the photons of light on top of each other because it's not limited to the spaces available in a fixed grid like an image but they are hitting the imaging surface much closer together now and so they produce an image that's brighter. Like how a magnifying glass makes the light passing through it brighter when focused.