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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.