That's the only method of backup / restore.
https://support.microsoft.com/en-us/account-billing/back-up-and-recover-account-credentials-in-the-authenticator-app-bb939936-7a8d-4e88-bc43-49bc1a700a40
If that isn't working then you can turn off 2 factor at the service provider end (each account) then install authenticator on new device and set up again.
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