I'm running two different GNU/Linux distributions, none is Debian-based, and they are both "pure 64-bit", so no multilib installed (which is necessary for Steam because it's 32-bit). But I wouldn't use Steam anyway. It would be nice if there was a generic Linux 64-bit release which is not bound to a specific platform/distribution. This of course depends on the libraries used to develop the game (most do work on GNU/Linux).
I realize I am a minority though. You probably won't have many requests like mine, and if that's the case, no need to bother. At any rate, your game looks really interesting.
I realise it is not exactly the most convenient solution, but have you tried to just export yourself a generic godot 4.2.2 binary and use it launch the pck file? That is exactly what I have done here and if it works just fine on ARM Linux distro, I am sure you could easily manage it on other distros you use.