The Steam Flatpak has been an adventure, to say the least. I added a second SSD just for games that gets automatically mounted on boot, and I gather that having the games installed somewhere outside of steam's /home/ directory was not jiving with flatpak's security model. It took some non-trivial editing (thanks, flatseal) to finally let the Steam flatpak be able to write outside of its own directory and install the games.
I still get occasional weirdness, especially on older games. I wasn't hearing any sound effects on Team Fortress 2, which I eventually discovered was tied to an selinux alert. At last check in, I still can't launch CS:Go, because of some backend problem while trying to play the opening movie...