It's worth looking into Lutris for non-Steam games as well. Comes preinstalled with Bazzite (heavily gaming-optimized Linux distro), though I don't have any non-Steam games to try it on since Steam works fine for all the games I play.
Also want to add that you can add a non-steam .exe and install some windows applications too, not just games. After installing you just remove the installer from steam and point Steam towards the installed applications .exe
Just make sure to tell Steam to use proton to run it. By default, it does not turn that on.
Yes, you can either add external games inside steam and set their compatibility options to use some version of proton or use proton through lutris or manually.
Proton is Wine but tweaked for the sole purpose of running games, so it packs a bunch of extra stuff needed to make games run well together.
Usually there's also a long list of per-game tweaks and changes to make sure it runs, it's all preconfigured so you press play in your launcher and it works. Not need to change settings whenever you want to play a game.
You can still use regular Wine but you'll have to set up a bunch of stuff yourself, and eventually you run into a game that needs a different version of something that breaks another game, you get into prefix management and it's a mess. Or oh this game runs better when we pretend to be Windows 7 but this one works best with Windows 10. Proton just does it all for you, every game gets its own space with all the correct settings from the get go, and you just launch into the game and play.