Some multiplayer, but not all. Not that that makes it perfect, but I've had minimal issues with multiplayer games. I do not play popular FPS games where anti cheat software is prevalent, so that's mostly why. I did get Ghost of Tsushima the other day, and that is not compatible for online play, but I think that's because of Sony.
Wonder if there's any chance the Steam Deck / Linux market share is getting large enough where gaming companies are having to seriously consider fixing this.