Inside is one of my favorite games. It's not free (I think it's a one-time $3.99 purchase on the app store), but it's an action/horror platformer with a lot of puzzles. The plot is kind of up to interpretation: there's no lore explanation and a lot of people chalk it up to symbolism. The atmosphere is chilling, the gameplay is super simple, everything about it is just an extremely interesting experience. It's from the same people who made LIMBO if anyone is familiar with that game
The link to purchase it on Steam:
https://store.steampowered.com/app/304430/INSIDE/
Another one that I've enjoyed is Oxenfree. It's a supernatural thriller. You have to explore a military island's cryptic past after an overnight party-gone-wrong, and it has multiple endings depending on which course of action you decide to take as you solve the mystery. I played it on my phone but you can also play it on PS4, Linux, Windows, and Xbox
The link to the website, where you can purchase it for different platforms:
https://nightschoolstudio.com/oxenfree/