I personally find Balatro, on Steam (is most likely already in the package repo for your distro), to be addicting enough for me at least. Don't know if the demo is still up, but if it is, I'd start there to make sure you don't have buyers remorse. Works with Proton (right click on full game or demo in library, properties, compatibility settings, force them on, and I found it works with Proton experimental if I remember correctly).

Game is simple enough to play. Get hand of 8 cards. Play poker hands. Get chips based on hand. Win and get money. Use money in shops to buy things that change your deck or buy joker cards that do different things to the hands you play. Repeat for 8 rounds of 3 blinds, each time the required score going up.

That, or Baba Is You if you want a puzzle game that will warp your mind. Works out of the box on Steam, Proton not required. Complex game where you control character(s) and/or object(s) to try and get to the win condition. The catch is you have little text words that take up tiles on the screen (can turn tile outlines on in settings if it makes it easier to see and understand, which it does for me). You can move them to change the rules of the game. You might start off controlling Baba, the rabbit(?) creature the game is probably named after, then switch to controlling all the walls in a level.

Has a built in level editor and even has bonus levels from the developer that show off things added for the level editor and scrapped levels cut in development, some with signs that give commentary.

Though, for non-Steam games, I personally like to recommend games like SuperTuxKart (don't know a single mainstream distro that doesn't have it in their package manager). Game starts you off, if you start the story mode that is kinda just there, with a tutorial that teaches you how to play. Simple enough racing game with a ton of community made add-ons for when you get bored of the official content. Has online multiplayer and can be played with friends through split screen so long as you have enough keyboards/controllers. Don't know the max amount of split screen can support though.

I've played enough of all three games that they aren't as addicting as I have either played too much (SuperTuxKart and Balatro) or I've gotten to the point where the puzzles are tedious to the point I spend a few minutes on them before giving up (Baba Is You)