Board Game Arena

Looking for one where the rules aren't too complicated or too wordy.
So far, these are the ones I know:

Kingdom Builder: too sensitive to luck
Railroad Ink: zero player interaction
The Builders: Middle Ages: not many players, can't undo entire turn
Reflection: dexterity game

Any others?

Khronos: Very few players, but only 7 turns. I think rules look much more complicated (with all their special tile names) than they actually are.
Break the Code: Deduction game.
Finity, Homeworld: Abstract 2-player games, there can be a lot of thinking time here, but maybe not too few turns.
Wingspan: 26 turns, sometimes you think for quite a while.

If complex fixed-round-count worker-placement games were an option (I guess not, since you ask for simple rules): Barrage, Carnegie, Tzolk'in, Madeira...

GORami, Break the Code.

I also throw 7Wonders in the ring. Very short games with fixed 18 turns but you can think a lot about your turn. It seems like it's a lot to learn but for most people, it is easier than perceived at first glance. But it might be too much luck involved for your taste.

Santorini?! No luck involved.

Castles of Burgundy! The rules aren’t complicated, and although there are many different tiles, the game on BGA has a very accessible player aid on screen. There is a fixed number of turns, so the game won’t be too long, but enough variety for you to scratch your head thinking what your move should be.

Dungeon Twister. Abstract game packed as a Dungeon Crawler / Brawler game. Rules aren't too hard, not that many turns in a game, but due to the rotating of the rooms and amount of possible combinations, very prone to analysis paralysis.

Progressive Chess fits what you describe,

https://en.wikipedia.org/wiki/Progressive_chess

although as far as I'm aware, it's not on BGA.

Bandada and Pier 18 are the best examples, in my opinion. Very few turns.

Other games that may fit it:
Cacao, Potion Explosion, Get on Board, Next Station, Rallyman, Happy City, Shifting Stones, Connect 6.