I used to play Unblock Me. Made it maybe 1000 levels in various difficulties before stopping.

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!

Assuming that you have Netflix, open it, scroll to games and open the section. There are tons of great games without any microtransactions or ads. They're overwhelmingly commercial games licensed by Netflix.

Pixel dungeon, but it's not really low stress.

2048. Though im sure that one has ads. Probably depends on what you grab from the internet, as usual.

Mobile games suck.

Monument Valley and Gorogoa are both excellent and free of nonsense.

Both are available on mobile and Steam. Gorogoa also on GOG currently 70% off.

Meant to link monument valley 2: https://www.monumentvalleygame.com/mv2

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.

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

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

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.

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.)

Soko++

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.

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.

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.

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)

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.

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

Cell to Singularity is a great little mobile game that does have microtransactions but are easy to ignore/avoid. I played through it several times and may need to dust it off for another playthrough. Great music too.

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

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

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.