Yes, what's really needed is for Itch to provide a signed token giving the user's account ID (and possibly other details if the user agrees to share them). I know there is a way to use such a token with Firebase and probably there is with PlayFab too.
A related problem is that there is no way for an HTML game to know if the user has paid. I will soon be uploading a new version of Gwen which will be chargeable after a short taster. It interfaces with PayPal entirely on its own because while I could set the game page to accept payments, there is no way for the game to be notified of them.