Looking for a casual game that I can quickly pick up or put down

Any turn-based strategy game could be good - you can stop playing Civilization any time you want, right? There's no need to go one more turn

Not so much a game recommendation but a platform, but if you don’t already have a Nintendo switch, it might suit your style.

It lets you suspend any game at whatever point by just going to the Home Screen. You can then put down the switch and leave it for days or even weeks at a time, and then you can just turn the switch back on and pick up exactly where you left off in like 5 seconds.

I’ve been playing heaps of the new Zelda game, whenever I get a spare moment, but also if Nintendo games aren’t your style, nowadays there’s quite a good library of other games for the switch now.

Obviously the suspend feature doesn’t work for multiplayer games though, and to be honest I’ve found multiplayer in general doesn’t work as well on switch as other platforms, but it really is great for quick sessions of single-player games.

Also being portable is a great bonus

Slay the Spire comes to mind.

I have Trackmania Stadium for that. Going into a full speed server (Only need to steer left or right while constantly press forward) and put some music up.

The flow of the race tracks together with the music is very nice and because no speed control is needed, no need to get into the physics and tracks to enjoy the game.

I can recommend to get into Trackmania when you have more time, the feeling of mastering a hard track is marvellous, but just speeding around is also fun as hell.

I always see people recommend Stardew Valley in these threads.

Simon Tatham's Puzzles is an amazing collection of little puzzle games. There a ports for both Android and iOS available as well.

Seems you're into puzzle games so I'll recommend you that there's an entire genre of minesweeper clones / inspired games on Steam. Some are straight up clones of the game, others are very similar, and some use the mechanics but twist them around in interesting ways. Good examples are Hexcells, Hexseed, Tametsi, DELETE, and GlobeSweeper. Once you learn the basic mechanics, they're pretty hard to forget, and a lot of games borrow mechanics from others. When I started DELETE, for instance, the mechanics were a little bit different in some small ways, but I pretty much rocketed through the first dozen levels because of my prior knowledge of how minesweeper works.

There's a little game called Dorfromantik in which you build a map with tiles. The PC version is my go to game when I need to multitask (made long Teams meetings during covid bearable). It's very simple, yet I have like 150h put into it. Not even that expensive to buy.

There's also a board game version which apparently ok too.

I really enjoyed Shovel Knight Pocket Dungeon. It's on PC and consoles, but if you have Netflix on your phone you can play it there as well.

Mechabellum.
Very easy to pick up auto-battler. Short matches, but quite a lot of tactical depth.

Counter Strike Surfing. Doesn't really matter whether you play for 10 minutes or 2 hours :)

Into the Breach would work. You can turn off the game at any point and come back to it, thanks to it saving after every turn. Plays a lot like chess, with different abilities and enemy types to keep things interesting. Highly recommend!

I'll throw out Bad North. It's a little strategy game that features scenarios that last 4-5 minutes at most.

Brotato. Ridiculously addictive auto shooter with one minute waves. I play it in my downtime at work. There are interruptions with zero warning and it's always easy to come back to later.

Minecraft java version for mod support. If vanilla doesn't hit there are thousands of mods and modpacks to choose from for very different experience

Gonna be a bit of an out there recommendation but old Popcap games are available on Steam. They're good casual games if you don't mind the lack of challenge. I personally like PvZ, Zuma Deluxe and Feeding Frenzy 2

I'll second the recommendation of Dorfromantik, and I'll also add Islanders, which has a similar vibe but different visuals and gameplay.

In both cases, you're given pieces that need to be placed on the map in order to score points, and that's the extent of a round, which makes it very easy to play for a couple of minutes, then put it down until later.

Overwatch 2. Since the changes from old Overwatch, there is no real point in anything other than Quick Play, which means 5-10 minute games, and you are free to leave at any moment

i think Downwell meets your criteria, its pretty actiony but easy to put down

Vampire survivors. I swear it’s one of the very few games that I found actually fun in the last 5 years

Bloons Tower Defense 6 is easy to get into and also can return to the level if you quit out.