Short answer, you're shit out of luck with Google Authenticator.

I recently switched phones and installed Google Authenticator on my new phone. I restored my backup from the cloud onto my new phone, and all my apps and data were there for most apps. Not Google Authenticator, however. I followed all the steps that Google provides in order for me to backup my keys, but even through that, my data for the app were never restored on my new device, no matter how many times I would reset and restore the backups.

Needless to say that I am now using Authy.

And I'm still locked out of several accounts because of this issue from when I lost my last phone before I replaced this current one... I've reached out to Google support and forums regarding this matter, and it seems that there is nothing anyone can do to help me recover the keys to a new device for the 2FA that I've set up that didn't have their 16-digit keys available when scanned initially.

Sorry, and I hope that your data is able to be recovered. And solely use Authy moving forward lol