> Not to mention Google Authenticator deliberately prevents these stored tokens to be backed up and transferred to a different device, which makes upgrading devices troublesome.

It doesn't offer export in the app UI. It's not doing anything to prevent you from backing up the tokens yourself; they're stored in the clear in the sqlite database for the app.

If that's too much for you, there's a good chance https://github.com/puddly/android-otp-extractor can get them automatically.