If you're fine playing single player, you can try 2009 scape.
RetroGaming
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Forgot about this, thanks!
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.
I can't speak for Civ III, but my experience with Civ V is that running the Windows version under Proton actually performs better nowadays than the native build. But YMMV.
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
TIL poker night at the Inventory has a SFW version
Seconding Universal Paperclips, it gets crazy with the shit you unlock!
Idle games! So many idle games.
I would say A Dark Room is way too interactive to count as an idler, though it has idle-like elements, sure.
My go-to for this is Stardew Valley
Doesn't Stardew have timed days?
Yeah but you can pause if you want. As long as it’s single player.
Then in that case, I'd suggest FTL: Faster Than Light. You can literally quit the entire game mid-battle and continue right from that moment; every single moment is saveable.
You can pause!
Balatro is my rec.
For a truly low-attention game, I suggest ProgressQuest. As a bonus, it runs great on Linux, too!
Interesting that it doesn't support HTTPS, given how it has an account website.
Kittens Game, Kingdom of Loathing, and Cookie Clicker also work, though not as well.
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.
Peggle
I often play "update open street map". Gotta get the lines just right, add some text, and everybody wins.
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)
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.
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.
Good lord calling banished chill is insane haha. It has to be one of the hardest city builders me or my wife have ever played.
Maybe I spoiled it for myself by playing as many city builders as I have, but I didn’t feel it was too hard the one time I played it, just really slow to get things rolling.
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...