I can't address the primary concern here but the app I switched to for 2FA named 2FAS is able to back up all your codes in case the device gets affected. Either

I can't address the primary concern here but the app I switched to for 2FA named 2FAS is able to back up all your codes in case the device gets affected. Either to Google account or a file. Google Authenticator did not have this option until recently I believe.