A lot has been said in recent days and weeks about iPadOS 16 Stage Manager currently being used by beta testers. Some folks are finding it very buggy or just having difficulty with the design of the new feature. It’s far from perfect, no doubt about that. I’ve been bouncing back-and-forth between using the feature and then turning it off to go back to the default split screen multitasking. There’s much to like about Stage Manager and for the most part I’m enjoying it. If not for the buggy resprings I would likely leave it on.
I found that for myself, it seems to work best with the dock, turned off, and the side multitasking strip also turned off. Even the larger 13 inch iPad is still a relatively small screen so by turning those off I’m getting a bit more room for window content. I think the greatest potential for this new feature is probably with the 13 inch screens or something larger that might come in the future. Also it’s great on an external monitor which I use a couple hours a day.
My favorite use thus far is 3 windows side by side taking up the full screen. Two groupings in particular: Spring for Twitter, Twidere X open to Mastodon, and Gluon for Micro.blog. Another 3 windows set-up is Mail, Slack and Messages. In general I like the width of 3 windows side-by side on the 13" iPad Pro.
What would I like to see changed? Like many have commented on, when changing window sizes pre-determined window sizes are chosen for the user rather than fluid free form window sizing, and that can get to be a bit tiresome instead of being helpful. In my use it requires me to do more work than I should have to rather than less. Personally my preference would be to have free form window sizing but with a grid like snap to feature  similar to that found on  Windows. I would imagine half screen, quarter screen, and 1/3 screen, those sorts of size options. There are similar third-party apps available for the Mac that seem to be popular.
Also, when switching apps sometimes things can get a bit confusing, especially when using an external display.