Games

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.

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.

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

Emulating a Nintendo DS and looking for stylus only games is my recommendation. Games like Kirby Canvas Curse, Kirby Mass Attack, and Warioware Touched are fun.

Word Cookies. I absolutely love it. You can pay for things, but it is absolutely not necessary and is basically only if you feel the need to use boosts that allow you to cheat your way past the level. I think it costs $2 to go ad-free.

It does give you regular popups asking if you want to buy coins, which I admit is annoying, but they are unnecessary to enjoy the game. There's also endless opportunities to get coins and other boosts for free. I have something like 80,000 coins and dozens of boosts and other than the $2 to go ad-free, I've never given them any money.

You do have to have certain word skills to enjoy it as much as I do. If you're the sort who can crush it at Boggle, it's the game for you.

I play chess, mahjong on mobile.

There's also final fantasy pixel remasters, Baldurs Gate, planetscape torment, shadowrun games and trials of mana on mobile too.

Walk master

Cosmic Combo, an iOS port of Johan Peitz’ PICO-8 game Cosmic Collapse, is good.

Star command, anomaly, world of goo, EDGE, knight of pen and paper...

These are some good ones I got from humble bundle over the years but many are quite dated so not sure if they're still around. No BS microtranactions

Emulation!

Sparklite, I don't know what it looks like purchases-wise, it was free with gamepass and had no in-app purchases when acquired that way. It's probably one of the newest games I'll post about. New enough that it was possible to get it with gamepass, lol. The game sort of has a modern retro zelda feel. I don't think it's a particularly long game, but it's certainly enjoyable and pretty casual. I think if it has transactions, reading other reviews it might be like a "purchase the rest of the game" style thing. So basically a free demo that you can then choose if you like the game enough to pay.

Out of the Dark is alright.

Antimatter Dimensions

Gubbins is a fun word game, it's a one time purchase and apparently part of the profits go to charity due to Hank Green investing in it in a creative way.

Imagzle. There are "buy more levels" but there are plenty on the main one. It gives a picture, more or less, abstractly related to something. Art, movie, book, many random things

Potion Permit is about $7, but pretty fun. If you got $10 to spare, Ex Astris is a jrpg that's pretty good.

I played a cool one called Pirate solitaire, very charming

royal match has no ads at all, its pretty fun just gotta ignore the microtransactions which is pretty easy to do at least compared to other games

You can get a port of space cadet pinball from GitHub!

Old School RuneScape potentially fits this description

Gardenscapes is the original match 3 and build a mansion and is still my favorite. There are micro transactions to get additional power ups, but the fact that they are constantly updating with new seasonal events and you never run out of levels