Bazzite is based on Fedora so you can get alot of the same tooling setup to run your games without the inconveniences of Bazzite. Get protonUp-Qt (if you end up using KDE its in the discover store) and use it to automatically install Proton-GE for you. GE is an improved version of Proton made by GloriousEggroll, it should work with almost every game on Steam.

If you have games outside of Steam I recommend HeroicLauncher. I could never get Lutris to work, but Heroic just works for me. It can also use Proton-GE with non-steam games.

Alternatively you can just add non-steam games to Steam. You can even install Windows only launchers like Battle.net on Linux using Steam and Proton.

The website for finding out which games work on Linux and what customizations might be needed for best performance is: https://www.protondb.com/