Slay the Spire has a decent mobile version. Not sure about the casual part, but at least it's turn based

Stardew Valley and Terraria may both fit your list, although Terraria stresses me out a bit.

Pixel Dungeon: Roguelike, infinitely replayable. https://play.google.com/store/apps/details?id=com.watabou.pixeldungeon

Auralux: A simple real time strategy game. https://play.google.com/store/apps/details?id=com.wardrumstudios.auralux

2048: Simple to learn, difficult to master puzzle. https://play.google.com/store/apps/details?id=com.androbros.puzzle2048eng

One time purchase:

• Peglin ✨
• Luck be a landlord ✨
• Forager
• Dicey dungeons
• Dead Cells (optional DLC)
• Bloons Tower Defense 6 (out of the way IAP) ✨
• Terraria
• 20 minutes till dawn (has a non premium option with some micro transactions)

Free:

• Antimatter dimensions (long idle-ish game) ✨
• Legends of Runeterra (just play the story modes) ✨
• Team fight tactics (cosmetics only)
• Plague inc (and probably rebel inc, but I haven't played that yet) ✨
• Super Auto Pets (cosmetics and extra optional sets) ✨

Star on the ones I'd specifically recommend for casual play

Games I know of on Android:

• Ganz Schön Clever — Digital adaptation of a board game. It's like bingo except you roll dice and there's actual skill involved.
• Knotwords — Crosswords but instead of word clues, each region of the board indicates what letters appear there.
• Threes — 2048 was a ripoff of 1024, and 1024 was a ripoff of Threes. Threes is the OG.
• Sagrada — Digital adaptation of a board game. Build a stained glass window by rolling dice and placing them on your board in the right pattern.
• Simon Tatham's Puzzles — Big compilation of various puzzle types.
• Handshakes (by Pet Pumpkin) — "Solo co-op" sokoban puzzle where you try to get two guys to shake hands.
• inbento — Assemble lunch boxes by sliding tiles around to match the reference picture.

I use Privacy Friendly versions of Sudoku and Minesweeper on the F-Droid store. I also really enjoy Nonograms (aka Picross), and haven't found a good foss app for it, but the app "nonograms.com" has been a good experience for me. I paid like $5 for the ad free version and that's been it, nothing else.

I liked egg inc for a while, if you're looking for clicker type games.

Other than that I can recommend

• Stardew Valley
• Peglin
• Sudoku
• Nanograms
• Dungeon Village 1 & 2

Multiple of these are paid, but I'm 100% on board with paying a small amount for an app rather than paying a multiple of that for in-game Battlepasses and whatevers.

It annoys me a lot to say this, but Netflix has some excellent games in their roster. So if you have a Netflix subscription, check those out. I personally very much enjoyed

• Storyteller
• Into the Breach

But they also have ports of some very good PC games like Spiritfarer, Terra Nil or World of Goo.

I had nearly given up looking for good mobile games when I remembered that emulators exist. Nintendo DS games map pretty well to a smart phone, there are some games that use entirely touch controls. I'm using the MelonDS emulator and I've mostly been playing advanced wars: days of ruin and puzzle quest 2. Puzzle quest is pretty excellent and chill by the way.

@PlzGivHugs Unciv, neat open-source turn-based 4X, obliviously inspired by the Civilization series

Mini metro Mini motorways

I may or may not have opted to ignore the stress part.

My recommendation l is going back to the basics: chess, especially lichess.org

You can choose a mode however you want, and it may or may not be stressful. Multiplayer with friends or random online people, choose a time between 30 seconds for a game and infinity to move.

If you don't want to play right now, you can solve tactical exercises.

Mindustry is amazing, and free somehow

If you like the older Pokemon games and can get the ROMs on your phone, PokeMMO is really cool. It's an emulator that turns the first 5 generations of games into an MMO where you can take the same character across each region.

There's a handful of changes to the base game, but most are small: Berry farming is changed, there's an Exp Share for EVs now, Sweet Scent is used to summon a 1v5 against wild Pokemon... There's character customization... There's some QoL stuff like shiny encounters having a sound effect and adding a confirmation box so you don't accidentally flee, and the stats page for your Pokemon is way more detailed.

In my experience the relatively small selection of the F-droid store is full of these type of games.

Troll patrol

Sudoku

Unciv

Shattered Pixel Dungeon

Pirate Solitare

..just to name a few All full versions, no ads or premuim options. Love F-droid, its a shame the selection is quite small.

The website https://nobsgames.stavros.io/ helps surface these, and let's you filter out based on different things.

One that I like in particular is Gauguin. It's a Sudoku-like with different math-y rules.

Anuto TD is a tower defense game that is also really good, but not so low stress.

Lichess, if you're into Chess. It's a great, no compromise, high quality app. Stressful if you get too worked up about competitive, but puzzles are at least relaxing.

Holedown

You just aim a ball and clear blobs before they reach the top. No timer. I usually play this with my screen split to YouTube.

I'm seconding Simon Tatham's puzzle collection, Nonograms Katana, and Stardew Valley, all of which are in regular rotation and fill different niches in my soul.

Stardew Valley is casual, low stress, with heaps of content.

For quick few minutes I've recently been into Pirate Solitaire which is on F-Droid.

Try searching on https://www.darkpattern.games It seems like a vast collection with reviews aimed at finding and naming healthy and unhealthy games

Stardew Valley has been out on Android for a while now.

Hoplite

Man mobile gaming is such utter crap in general, I hope the handheld gaming PC trend picks up and people start developing actual competing games for Android instead of micro transaction filled pay to win pieces of shit games

The original Peggle. There's a free APK available on speedrun.com. Works flawlessly even on modern Android.

https://www.speedrun.com/peggle_deluxe/resources/ehelq

This isn't exactly what you asked, but I highly recommend emulation. I have had ePSXe downloaded on every phone I've had for the past ten years to play PS1 games. There are so many good titles, all of them free, playable offline. You might like Intelligent Qube Mr. Driller Devil Dice for puzzles. I love playing final fantasy, legend of dragoon, suikoden, Spyro, crash bandicoot. I don't care about graphics, but I am a sucker for playing through a story.

Tetris

Nonograms Katana. I guess there are micro transactions for useless crap but it's not pay to win. If you're on iOS, it's just the puzzles but if you're on Android, it includes a "mini game" where you...build out a village? And fight monsters in dungeons? It's really weird....but I'm in it for the puzzles.

Why don't you try emulation? Most phones nowadays are capable of emulating easily up until Gamecube

Blooms TD 6 - fun tower defense game with solid progression and everything can be earned by playing what I think is a reasonable amount.

Magic DosBox, not a game. But in combination with https://www.old-games.com/ , it's a pretty good selection of all the old games made for Dos back in the wild west of indie games back before they were even called that. There are, of course, also old commercial games that have transitioned to freeware now too. Should be able to find lots of awesome games there. Moraff adventure games are particularly interesting. Bit of a steep learning curve, but great to come back to now and then. The site has reviews of every game and sorts them into categories. It can be a little overwhelming just due to the sheer number of available games, but take it slow, and work your way through. It's worth the time investment to find gems.

You can check out whatever is available on F-Droid. I personally enjoy playing Freebloks once in a while, it's a mobile version of the Blokus boardgame

An alternative is checking out itch.io, searching with the proper tags, like puzzle, might yield decent results for your tastes.

You can also get Cookie Clicker or play the web version

Slice and dice