Why not use an open TOTP app like AndOTP. I use it all the time for sites that claim to require Google Authenticator, it works, and its easy to backup the secrets as plain text or encrypted with a password. I keep it current on my primary phone and a cheap offline backup, in addition to backing up the encrypted secrets file.
I use Authy on iPhone and Mac. I am looking for an OSS replacement but would not want to setup everything from scratch after I change device reinstall the app like Google Authenticator.
I've wanted to get off Google Authenticator for awhile now, mostly because of the backup-restore problem, also a general trend of limiting my involvement with the company.
Bitwarden does a decent job of storing and syncing TOTP codes. Make sure you always use a long password with Bitwarden though, to avoid a known and unpatched issue with their password-based key derivation.
