Grace,
Thanks for the confirmation that what I suggested for individual users of Microsoft personal accounts actually worked, since I'd suggested deleting the existing authenticator method and setting it up again from scratch in one of my fist posts in this thread, though that was before I learned that most posting here were actually using Work or School accounts in Azure, where the same process requires an administrator.
Deleting the authenticator method from your personal account should completely remove any remnants of an old phone for that account, resulting in exactly what you experienced as the process sets the new device up using the same steps that would normally have occurred for any new phone.
The 'loop' in this thread is apparently always caused by leftover remnants of an old phone, while the biggest problem for many is they're not the administrator of their own Work or School account and in quite a few cases no one in the smaller businesses often involved truly knows how to use or possibly even access their organization's administrator account.
Rob