Game developer here (not for this game).
It sounds like an anti-virus program/Windows Security is stopping the game from writing to files for you. That happens sometimes for games that do not have a high amount of users (~100 000 users), since only well-known programs are let through anti-virus programs and Windows Security.
I would try this if I were you (it usually solves everything when it happens to me regarding other software/games):
1. Go into Windows Security and into Virus & threat protection, then exclude the game .exe file AND its entire game directory there.
If you have an anti-virus program other than Windows Security, do the same thing there (for the .exe file and for the entire game directory).
2. Run the game and/or itch as an administrator.
3. If it still does not save, restart your computer, as anti-virus programs (and Windows Security) sometimes has a file or directory blocked until you restart your computer.