Just staring a loading screen essentially, most games will let you click around on the menu still and look at your skins or your settings or whatever. TF2 lets you queue mid match to find another game so you can play on a community server while you wait, and overwatch does let you do warmup DM last I remember (which was years ago so it might have changed). Can’t really think of anything else another game does off the top of my head.
You can run most games on Linux, you just have to enable proton, the steam deck uses a custom version of Linux by default, so at minimum anything marked as playable will work on Linux.
Also I never had to deal with drivers at all when setting up linux, but I’m not sure if that’s normal, I’ve only used Linux mint, which was pretty easy to set up.