You can't beat "Simon Tatham's Puzzles" for a FOSS puzzle game app. 40 logic and puzzle games. Super simple UI, many puzzles have parameters to customize the difficulty in various ways. All come with detailed explanations of the rules or mechanics.

Various ways to get it. But I think play store is preferred. The f droid repo gave me a compatibility warning when looking it up just now.

https://play.google.com/store/apps/details?id=name.boyle.chris.sgtpuzzles

https://f-droid.org/packages/name.boyle.chris.sgtpuzzles

https://github.com/chrisboyle/sgtpuzzles

https://www.chiark.greenend.org.uk/~sgtatham/puzzles/

As much as I hate NYT for MANY reasons, I've yet to find a better crossword.

Someone else recommended Baba Is You. Highly recommend that too

Shattered Pixel Dungeon is a really good, well polished, roguelike. It may be on the fringes of your request, it's not really a "puzzle" game, but you do need to think a lot to weigh your options constantly.

Free, no ads, no dark patterns.

It's been so long since I played a game on my phone but recently for nostalgic reasons I went looking for Myst. Not sure how well the puzzles hold up to adult me but i really enjoyed it when I was a kid.

There is also The Room which reminded me of Myst that I enjoyed.

I don't know what a "not_pron" style game is so I don't know if my suggestions are relevant though.

I like to play nonogram once in a while.

For "not pron" style: rusty lake series

Sokoban style: baba is you

Depends on what you consider "lateral thinking".

My first recommendation would be cardgame roguelites (Slay the Spire, Balatro).

F-droid has some good logic puzzles (Soko++, Sudoku)

You can play all of the games posted on !dailygames@lemmy.zip right in your browser.

There's an interesting game I got from fdroid recently called everest

What do you mean by "not pron"?

Simple Solitaire Collection has lots of different solitaire variants. No riddles, but you do have to think a lot. "Napoleon's Tomb" and "Simple Simon" are two interesting variants I learned about from this game. (Simple Simon has simple rules but can be incredibly hard.)

Free, no ads, no dark patterns.

See if you are smart enough to turn the thing off.

2048 will burn at least an hour. It's free, there are tons of clones.

You could play jackbox with twitch streamers.