On Windows or Mac, simply copy the "save" folder from the previous version's folder and paste it into the same location in the current version's folder. Unfortunately, on the web version, I think you must have done something that cleared the browser's memory.
Viewing post in Spy Bunny Luna v0.6 - Virtual Dungeon comments
its downloaded on the itch.io app on mac so i am not quite sure how to do that. But when i downloaded the update i now get a prompt (after selecting the 6.5 update) showing 2 game apps. One being the new version (with no save file) the other being my previously saved data but its not the new version (its still the 5.0 version) 