Just got it two weeks ago. Darkest Dungeon and Disco Elysium mostly. I tried a few oddball titles that I was curious to see how well they played. It's hit or miss but that's expected. Strategy/map heavy games aren't likely to play well on any console controller.
Since you're somewhat new, here's some general advice for having a good experience with unusual games:
For games that don't run well, be sure to check protonDB to see if there's any known fixes for issues.
As far as controls go, when a game doesn't play well with a controller, you'll want to check community control layouts. There are usually some really good layouts that make playing much more viable, even if it can't compete fully with mouse and keyboard.
I forgot about the community layouts!! Shame on me, i even own the og Steam controller that pretty much needed it for every title.
TBH I was just sort of testing out. I don't have a whole lot of need to play CK3 or Rimworld on a handheld but I'll check out my controller options for other titles.
Any tips on streaming games instead of installing locally?
I personally haven't messed around with streaming games, so I'm afraid I don't have much advice to give there. In addition to the native Steam streaming there are alternate streaming options like moonlight (if you have a nvidia graphics card) that might give a better quality stream.