Thank you for your reply, @keithcurtis!
I wonder if this is related to our ancient character sheet. We've been playing since roll20 came out and use this sheet still:
To reproduce, you collapse the sheet like so:
Then drag it off the bottom of the viewable page, "out of bounds" and as if you were going to pin it on your taskbar.
The deformation then happens, with the name plates free floating and the bottom player and macro bar moves up.
After more testing, this only happens when we do this on the lower border, not left or right or up. It's also not off the board (the map goes on for some ways).
It's truly odd how the AI summary describes some of this correctly (including how to cause it). Their fix only partially works, but it does work if you do it right. If you re-open the character sheet and collapse it again, and mouse-wheel scroll your screen up while dragging it, eventually the bottom bars and character nameplates find their way back to the right position.
I tried it with one more character and you can see the extent of the deformation here. Dragging the sheet off the bottom moves the whole roll20 HUD up, chat and all. Sybil's token moved up accordingly, but her flyouts are similar to where she was before.
It's so strange! At least a refresh fixes it, and it's not too hard to avoid doing this once you know to avoid it.