The appdata folder is separated from the game folder and i think it's not exclusive to the app, before i started to use it i downloaded the games directly via the site and i had an appdata folder. If i uninstall the game in my games folder, the files in the appdata folder aren't deleted, so if i re-install the game i get to keep my save files and my progression (read text), at least that how i understand it (i'm no expert hehe).
I remember buying a version of the game for like 5 dollars just before it went on hiatus last year (?), but i didn't have to buy the limited version of Lars special episode, i just downloaded it and now i wonder how could i do that if this version of the game apparently wasn't free....? And i don't remember if i downloaded it via the itch app or via the itch site but either way i got the game folder and the appdata folder so i don't know what else to say