itch.io

Yep your correct, it should instantly transfer your progress to the next update if you install the game. Even if you completly uninstall it off your pc or other devices as long as you devices still has the cookies of it it should still have your progress if you reinstall it.

You only have to pay once  and you can freely download all newer versions.

The game is really good my only complaint is some stuff is still in russian and is not translated to english.