You can restore from backup to another device (assuming there was one) but make sure no accounts have been added to the newly install app. Then sign on with recovery account to do the restore.
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.
There's no automated method to transfer to a different apple account. For this you'll need to turn off the two factor at each account service provider, then on the new device and using the new apple account enable the two factor at service provider's site.
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