You can recover your account credentials from your cloud account, but you must first make sure that the account you're recovering doesn't exist in the Microsoft Authenticator app. For example, if you're recovering your personal Microsoft account, you must make sure you don't have a personal Microsoft account already set up in the authenticator app. This check is important so we can be sure we're not overwriting or erasing an existing account by mistake. https://support.microsoft.com/en-us/account-billing/back-up-and-recover-account-credentials-in-the-authenticator-app-bb939936-7a8d-4e88-bc43-49bc1a700a40
For a microsoft work or school account you can manage (add / remove) devices here.
Without a backup to restore from the only option is to work with each of the service provider's account recovery methods. The authenticator app is nothing more than a code generator. The two factor is turned on or off at the service provider end.
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