If you play through Steam, since using Proton is enabled by default, you just need to install a game.

Sometimes you have to go into the game's Steam settings and manually pick a different Proton version if the game is old (usually an older version) or if the game is very new (Proton Experimental or gloriouseggroll's fork of Proton, ProtonGE, this one being a manual install from gloriouseggroll's GitHub), and you can find user reports on ProtonDB on what version other users have been using;

if you use Steam and GoG or other sources with no launcher, the main third party game launchers (Lutris, Heroic) use UMU by default, which means they leverage Steam's Proton to install and play games, basically doing what Steam does, just outside of the Steam app, therefore the experience there is the same as Steam.

This means that you can use most "normal" distros regardless of what they're marketed for. I've played games the same way on PoP! OS and EndeavourOS, simply plug and play (barring some edge cases).

Native, Flatpak or other doesn't really matter for the most part, though native is usually the most straightforward and hassle-free.

tldr: install any standard distro you like and Steam + alternate launcher and you'll find out that the gaming experience is almost completely plug-and-play