Google Authenticator has no encrypted recovery backups ;/

Check this out
https://authy.com/blog/authy-vs-google-authenticator/

Google Authenticator falls short when it comes to cloud sync options.
With Google, if you lose your phone you lose your access. Get a new phone and prepare to manually transfer your accounts, all of them, one at a time. This scenario alone seems to be the biggest reason people switch from GA to Authy.