Impressive start to the game! I'm already interested so I better ask about this bug immediately.
When I click on save here... (In Browser: Save icon at slot)
...I get this popup (prompt() is and will not be supported.. Aborting.)
I'm on PC and I'm using the itchio browser (launched from the official itch app). Exporting/importing seems to work fine, but I've never had an issue with using the save slots before in similar games.