Most of the games I play don't run on Linux sadly. Even Lethal Company, which is perfectly fine on Linux, couldn't be captured by OBS, so I had to switch to Windows before I could stream.
Game compatibility is getting better but still not good
What about with the new... thing. Um. There was a thread about it recently. It did... a thing. A Wayland thing.
Somehow, my exhausted brain managed to turn that into a reasonable search string.
Gamescope. A Wayland compositor that lets you define virtual displays that run overtop of your regular desktop.