Which steam do you use? I have heard that some people have issues with the Snap, Flatpack or Native versions. Also for proton there are different "versions" you can try, experimental or 9 is usually what I run.

    $ dpkg --list | grep -i steam
    ii  steam-devices                                               1:1.0.0.75+ds-6                      all          Device support for Steam-related hardware
    ii  steam-installer                                             1:1.0.0.75+ds-6                      amd64        Valve's Steam digital software delivery system
    ii  steam-libs:amd64                                            1:1.0.0.75+ds-6                      amd64        Metapackage for Steam dependencies
    ii  steam-libs:i386                                             1:1.0.0.75+ds-6                      i386         Metapackage for Steam dependencies
    ii  steam-libs-i386:i386                                        1:1.0.0.75+ds-6                      i386         Metapackage for 32-bit Steam dependencies

When a game doesn't work and the described symptoms happen, I usually try a few different Proton versions via the game's settings, but this has not helped me make a game run. If anything for some games it has reprocessed shaders or similar things that Steam games do before launching, maybe. But the result stays the same. Game is not starting, button changing back to "play" button.