Thank you very much! Ive been exploring my game files in my "File manager app" and I think I saw something about a save folder there! I presume I just need to copy that folder and place it on my laptop? Once I do that I can just recover the copied save file and paste it inside the downloaded game? But do you know what happens if for example the save file is for version "0.2.7" but the newer version is something like "0.2.8" will it be accepted or will it not work because it's an outdated save?
Yes that should do as a backup. As said, just make sure that it really contains everything (which based on the name it normally should).
The version thing depends on the game and what changes have been made. It could easily be compatible, but it could also be not or cause problems later on. Seeing as these are visual novels, I could at least assume that the saves should work as long as the dev only fixes some typos or something. But no guarantees on that, the engine used could also just say 'no', for example.