If you're fine playing single player, you can try 2009 scape.

Turn based games work the best for this, you can stop playing at any moment or resume at any moment without any issues. I played Civilization III for most lectures through university. Civ III does run under Proton but not well. Civ V has a native build, and would be a good entry point into the series.

Balatro, Slay the Spire 2, Poker Night At the Inventory, most Pokemon titles, Mewgenics, Worms titles, Plants vs Zombies (GOTY edition with widescreen fix), Poly Bridge

Roguelike games like https://crawl.develz.org/

Easier than Dwarf Fortress, still fun.

A Dark Room

Universal Paperclips

*cough*

For a truly low-attention game, I suggest ProgressQuest. As a bonus, it runs great on Linux, too!

Balatro is my rec.

Peggle

I often play "update open street map". Gotta get the lines just right, add some text, and everybody wins.

I've been replaying my favorite turnbased jrpgs from my youth. Working my way through final fantasy, beat the first three I'm on number four now. Also playing the og bards tale. Breath of the wild and the old ultimas are next.

Great on my steam deck during long meetings.

Polytopia is a pretty stripped down 4x game. Fun enough. Free too if you don't want to buy add-on factions, and it doesn't aggressively push you to buy which is nice.

I use dwarf fortress for this but the learning curve is pretty steep as it can be a bit complex but once you get the hang of it and you have a nice fort up and running, you can kindof let it run in the background like an idle game

the bazaar is a great async pvp autobattler - meaning no turn times or lobbies, pause and resume runs whenever (besides patches)

Banished is a pretty chill city builder game that could work well for what you want. The mechanics aren't that complicated which I find makes it pretty easy to put down and be able pick right back up where I left off. It's a Windows game but I've had no problems running it under Proton in Linux.

I was about to come in and recommend osrs but you got me lol.

Torn

Maybe Ragnarok Clicker lol, depends how low attention you wanna go but this basically doesn't need any attention

Edit: hmmm this game used to be on Steam...