Game compatibility and overall performance will be mostly the same regardless of which Linux distro you choose.

Yes some gaming focused distros add a few small extra tweaks bit in the grand scheme of things it's largely the same.

I wouldn't suggest using SteamOS outside of steam hardware het as its not built for general purpose computers. Futhermore, I wouldn't suggest using Bazzite (the steamos-like distro for general purpose computers) unless you were installing it on a gaming focused pc or htpc.