I notcied the "Bac Button" too, but we had some other last minute bugs to fix that we prioritised. The save state is done by saving a file somewhere at user:// with the FileAccess class. You can read docs and follow a similar example here. I'm glad you could gauge our theme implementation from the description, even if we're much more proud of how we got the story and ending into the game.
Thanks and good luck to you too!