Stage Manager is just awful, even on my 12.9".
1. You lose at least 20% of your screen to two docks now (yes I know you can turn off one or both if needed).
2. The visual difference between the angled, 3D appearance of the Stage Manager recent apps dock and the bottom dock is jarring.
3. There isn't much difference between what the Stage Manager dock does and what the bottom dock does. Stage Manager is presenting your last 4 recently launched applications, but those could have been presented in the bottom dock. When you add another application on top of an existing one, you are essentially creating an "app group", and again that concept could have been handled by the bottom dock.
4. The angled screen images in the Stage Manager dock are too small to be useful. I'd rather have just icons (which is already what the bottom dock does, and we already have a way to present multiple icons in a group in folders - just design a way to present running groups differently from a folder).
5. The name is dumb. A "stage" isn't a real UI thing.
I truly hope these are Beta 1 issues pending additional feedback and testing. That being said floating windows are so close to being amazing and that concept is transformative on iPad.