Can you export your 2fa codes from Google Authenticator in a format that is compatible with other autheticator apps with this new update? I don't see any sync option in the version i have on my phone and the play store isn't saying there is any app update to install so i can't see for myself.
Previously to export your 2fa accounts it would generate a QR code but those were only able to be imported back into Google Auth keeping you in the Google ecosystem and you couldn't even screenshot them easily to use 3rd party tools to get the info from those Google generated QR codes to a format that you could then use to import them to another authenticator app.
I now use the open source https://gitlab.gnome.org/World/Authenticator app on my PC as my main authenticator app when setting up 2fa as that give you multiple formats for backing up your 2fa secrets as well as generates QR codes that can be imported into most authenticator apps.