Oh lol, that is a lot. I’ve only used ubuntu, Debian, Fedora (i3 spin, which I believe had only dnf as a package manager), endeavouros, arch and researched nixos (which I’m definitely trying next) so I’ve never actually had flatpak preinstalled to my knowledge.
Sounds like a nuisance to get working so I don’t blame you for dual booting but it sounds it probably doesn’t know how to find the location of the binary it should be running.
Wait, what distros use flatpak by default?
Generally Steam let’s you use Proton on anything with a Windows version, regardless of whether or not it will work. You can also switch versions if needed.
I assume you’re missing a steam setting somewhere.
Mostly friends