Seconding this, steamos (or whatever is on steam deck) is just arch Linux with steam installed. They may have some extra little goodies in there... But nothing major. When you install steam on Linux, you can change a single option in setting and steam will download proton for you. You can attempt to run any steam game and most will work fine. Battlebit remasted isn't officially supported, but it's worked since day 1 on my arch install and I'm just using that since it's the most recent hugely popular game.
Yeah, multiplayer games with kernel-level anti-cheat are gonna be real hard to support on Linux. I don't know that we'll ever have a good solution to that.