I still suspect corrupted files need to be cleared out, if not with the Zwift app, then possibly with tvOS.
While the specific symptoms (passwords not being reset) differ from your specifics this previous thread suggests that a factory reset on the AppleTV might address your issue. Do you use the AppleTV for lots of other things besides Zwift? If no - it doesn’t take much active work, just time to let the box do its thing.