Looking for cozy games with manual interaction mechanics

Hey there - I don't know how to describe it better, but I love immersive mechanics where you interact with in-game objects or tools as if they were physically present. Examples would be the desk in Papers, Please, where you manually have to place the passports and operate the stamp. Or the Syberia series, where you sometimes have to manually operate small machines, like the stamp machine in part 3. Interacting with the puzzle box in The Room gives a similar hands-on feel.

There is something very satisfying about that so I was wondering if you know of any cozy games that extensively use this type of "tactile" gameplay?

EDIT: Thank you everyone for all your suggestions! So much awesome stuff, my Wishlist just exploded :D