They've directly stated that the itch.io version of the game is not supported and they have no plans to change that. It'll still get updates but they won't give access to the account system. They haven't promised that will never change, but there's no reason to expect it either.
I've spoken to Innersloth support and been directed to itch.io support to get my game refunded because I functionally don't have the full game any more.