Google broke that for their Authenticator some time ago.
This app https://mattrubin.me/authenticator/ works with encrypted backups.
Looked again and it seems like things changed sometime around 2015-2017. Sorry for the misinfo. https://dpron.com/recovering-google-authenticator-keys-from-...
Really? That wasn't my experience when I restored from backups. Had to set them up again despite most everything else carrying over.