Make sure to sign on to your recovery account before adding any accounts to newly installed app then 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.
https://support.microsoft.com/en-us/account-billing/back-up-and-recover-account-credentials-in-the-authenticator-app-bb939936-7a8d-4e88-bc43-49bc1a700a40
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