Yup, the difference between Ubuntu, Fedora, and Arch or whatever isn't going to be all that big, assuming you're working with each distribution's default kernel and running with a Steam's provider runtime. You might get 1-2% here and there, but that's pretty much within run to run variance anyway.

That's not all the factors that play a role in performance in games.

For instance, what fork of the kernel are they using? Are they using zram? What graphics driver are they using? Gamescope? Gamemode? All of those things affect performance of a game to varying degrees.

Also, Proton experimental is definitely not the default on any system, that would be Proton 8.