First one coming to mind for me is Pillar Hop. Very simple, chill, and just had ads iirc (I block them, but I'm pretty sure it does, anyway.)

Probably Scalak, a 3D puzzle game. It isn't foss and is paid.

Hmm, I was gonna say moonshades, last time I played it there wasn't much for things you could buy. But when I look now, there is. So I can't say for sure how unnecessary any of it would feel now, but it wasn't necessary back when I played last. It's kind of like the old early 3D party dungeon/maze crawlers where you use the arrow keys to walk one "block" at a time. There is only 2 party members in this. So you still sort of get the group synergy stuff, but each character is a bigger share of the team power. You could do a tank/healer thing or magic damage/melee damage, or not have either one focus on anything in particular.

I hope it's still not necessary to buy anything, it was a good game. But the store is pretty comprehensive now, so that has me worried.

Galaxy Genome, it's a space exploration game. Sort of a project to make a comprehensive 2D version of Elite: Dangerous. Or at least it started as that, I don't know if it has achieved and surpassed that by now. It was pretty far along last I played. And that was a while ago now. I kind of play games on and off for years, so that is mostly gonna be a running theme of all the games I post here. Games that you find yourself wanting to pick back up again, over and over.

If you don't mind a classic chess. Blitz/bullet/rapid/horde are different styles that don't take as long to learn enough to have fun. Chess puzzles or against the computer are available if you want to keep it strictly single player. Lichess for multiplayer or I like chess tactics pro for puzzles.

Crosswords, there are programs like alphacross that aggregate from other sources to try different puzzles to find ones that aren't too easy or hard.

I have lately been enjoying Legends if runeterra's Path of champions mode (PvE)

Old School RuneScape potentially fits this description

Grim Quest and Grim Tides. Two games by the same person. I haven't played Grim tides yet, but it's also free. Grim Quest is not a particularly large game, but I've still managed to play it over many years. I did a full run of each difficulty one by one. There is a bit to learn before it feels easy and casual, but it does get there. To be fair, I try to play it without dying. If I let myself die, it would be alot more casual even from the start. Dying is not heavily penalized on default settings, but you can alternately choose to play hardcore. Otherwise dying usually just means you gained less money for that run, and didn't make the game any harder. The game only gets harder when you successfully clear a dungeon. You can also just exit the unfinished dungeon without dying and keep most of what you have acquired so far on that run, minus a small fee for quitting the dungeon.

There are preset difficulty options, but you can also craft your own custom difficulty. There are things you could spend money on, I think it may have started out with ads. But I consider games with ads that you can pay to get rid of as basically a free demo, and getting rid of ads is the purchase price if you like the game. So they don't deter me if they don't basically break the game to add ads to it, or affect the flow of the game whether the ads are there or not.

Exiled Kingdoms, its an older isometric 2D adventure RPG. Kinda feels like it would have been made 30 years ago for pc, but it was made relatively recently for phones. I don't think there was any micro transactions. It may have had an initial purchase price, not sure. That's usually what I look for in a phone game. The traditional model of buying a game and then just playing a game. No gross mobile game stuff.

Alto's Adventure is a pretty chill game to play when killing time. https://play.google.com/store/apps/details?id=com.noodlecake.altosadventure

I also like the "connect the dots" puzzle games, like this one: https://play.google.com/store/apps/details?id=com.playvalve.connect.dots

Neither game requires microtransactions for the full experience. They might have ads, but my adblocker blocks them if they do.

Soko++

Not sure what sort of length on play you're looking for but wingspan and terraforming Mars are both really good board games that have good-to-quite-good mobile versions.

Mini Motor Racing might be a good match. It has some DLC available (additional cars), but none of it is necessary to enjoy the game.

Royal Match and Royal Kingdom are both add free and free to play. You can buy stuff, but you dont need to

Golf on Mars and Desert Golfing. Super simple. No ads. Its just 2D golf that keeps on going with any gimmicks.

Friends and dragons. It's a bit like easy chess with d&d style classes and species. It has transactions, but you can easily do well for free. I've been free playing for years (though I did throw them $10 around year 2 because of how much entertainment I got from it)

Some good games I recommend are Alto's Adventure / Odyssey, any bejeweled game, Cell to Singularity, Idle Slayer, Monument Valley, Reigns, Sky Force Reloaded, and Stick Fight Shadow Warrior. Hopefully that's enough!

I really like Usagi Shima. There is not much gameplay, but it's a nice game to just relax for a few minutes. Also "Really Bad Chess" is a nice twist on chess. :D

Loop hero is really fun imo! Also solitarica

bloons td6 is a nice cozy game, one of my faves

I made a post the other day about some gentle arcade mobile games which are currently free. I've only played Traffix so far, but it seems great.

If you are comfortable with games that are not technically classified as freeware yet, but functionally, they probably should be... then emulation of older consoles is a great way to go too. While they are certainly not "legal", I don't think anyone playing them has ever gotten in trouble. Only the people that try to make money off of it find that the console companies are motivated enough to shut them down. Otherwise, it doesn't feel super risky to just play stuff. Just stick with games that are impossible to pay for if you want to be completely safe. There was a ton of good games on 16 and 32 bit consoles that you literally couldn't pay for now if you tried. And even as new as gamecube is getting pretty hard to possibly pay money for.

Newer stuff, I only feel ok emulating what I actually own. But as time goes on, newer and newer stuff becomes the new old stuff. A pretty wide variety of console emulators for android are in a good place now.

I do recommend a controller though if you go this route. Ideally one of the ones that also holds your phone for you. Either by making it into a switch/steamdeck kind of shape, or the ones that hold the phone above an xbox style controller. Both are good.

If you have a Netflix account, you can get Bloons TD6 for free on Android. It's fun and the microtransactions are completely unnecessary and hidden away. Beware it's a battery hog though

Also, if you like puzzles, look up the various variant sudoku apps from Studio Goya, particularly the one called "Cracking the Cryptic"

Sky: Children of the Light

You get to run/fly/swim/dive around and explore several mostly chill realms, helping out "spirits" and collecting light (one kind for currency, another to increase flying ability), and optionally interacting and cooperating with friendly randoms from around the world. There is a story to it which I won't spoil, but there is always more to do even after playing through it.

There are zero ads.

There are some optional transactions, but they aren't pushed constantly (there are changing "seasons", and you can buy a pass for each one which will give you access to special cosmetics and the in game currency to buy them with, but there is plenty to collect without it).

Seasons also repeat (not exactly as they were, but the spirits from them return and their items become available again) so if you missed something the first time around because you didn't have enough in game currency, or you took a break from the game, you'll get another chance at it (I also think items that were initially only available with the pass you buy for real money, later become available for in game currency).

Keeping that in mind, you can grind as much or as little as you like, and there is also a limit to how much currency you can collect a day, so there's only so much grinding you can do if you are so inclined. If you're not that bothered about buying all the items, you can take a really relaxed approach and just play through the tasks and explore at your own pace (even learn how to play an instrument lol).

The first time I played it a few years back, I didn't really "get" the game, or think to look up any information about it, so was just randomly flying around and getting confused and frustrated when things were a little less chill at points, so I quit. But a few months ago I decided to give it a second chance and having actually taken the time to understand what is going on in the game, this time around I'm enjoying it a lot more.

Cardinal Quest 2, it is possible to spend money, but honestly spending money would be worse than earning the stuff yourself. I still probably gave them some money, since I think the game was free. You don't have to have played Cardinal Quest 1, it's pretty story light. Kind of like playing Diablo 2 if you never played Diablo 1. Kinda the same game as the first with much better execution after learning some lessons. The game itself is pretty easy, but there are optional challenges you can take on that can be as their name implies. Lots of replayability as there are many character classes and 4 different stories. Over time you'll likely want to beat each story with each class. Mostly cuz it keeps track, lol.

I'm enjoying isle of arrows right now. Tower defense but instead of having a set map and same towers you get to draw cards and have to make do with what you get. Some cards give you pathing for the mobs, other expand the buildable area, others give you towers. Simple and fun. Game pauses between waves so you can take as long as you want to prepare.