In short: add the option to show a QR code (or copy/paste able secret key) to move a 2FA code to a new device and/or authentication app, with the caveat that Authenticator will delete it once moved.
This retains the feature/security opinion that having the same code in two places defeats the point of 2FA whilst making moving codes a lot easier.
Migrating to a new device can be a big pain, often because many apps and websites don't support renewing 2FA codes without also reissuing backup codes (which then take ages to write down if you prefer that to keeping a bunch of risky text files somewhere) or disabling and then re-enabling 2FA altogether which is (pedantically) a security issue itself. Not to mention the flurry of emails and notifications you have to clear up after renewing two dozen or so 2FAs.
Currently Authenticator only supports migrating to a new iPhone with encrypted backups, which is OK but has some limitations - not everyone uses that backup method as it requires a second trusted device to back up to, and you need to have a recent backup. Some users might prefer to not have their codes backed up at all, given paper recovery codes are intended to be used if a device is lost.
Secondly, this would allow for portability which IMO is a good thing, to allow moving to a different 2FA app if a user wishes to do so.
Note also that the current policy of including codes in encrypted backups does mean you kan skirt the rule of not having the same code on two devices, so forcing a code to be deleted once moved using this suggested feature may be unnecessary/not really more secure, and instead the app would just strongly suggest deleting it once moved.
In short: add the option to show a QR code (or copy/paste able secret key) to move a 2FA code to a new device and/or authentication app, with the caveat that Authenticator will delete it once moved.
This retains the feature/security opinion that having the same code in two places defeats the point of 2FA whilst making moving codes a lot easier.
Migrating to a new device can be a big pain, often because many apps and websites don't support renewing 2FA codes without also reissuing backup codes (which then take ages to write down if you prefer that to keeping a bunch of risky text files somewhere) or disabling and then re-enabling 2FA altogether which is (pedantically) a security issue itself. Not to mention the flurry of emails and notifications you have to clear up after renewing two dozen or so 2FAs.
Currently Authenticator only supports migrating to a new iPhone with encrypted backups, which is OK but has some limitations - not everyone uses that backup method as it requires a second trusted device to back up to, and you need to have a recent backup. Some users might prefer to not have their codes backed up at all, given paper recovery codes are intended to be used if a device is lost.
Secondly, this would allow for portability which IMO is a good thing, to allow moving to a different 2FA app if a user wishes to do so.
Note also that the current policy of including codes in encrypted backups does mean you kan skirt the rule of not having the same code on two devices, so forcing a code to be deleted once moved using this suggested feature may be unnecessary/not really more secure, and instead the app would just strongly suggest deleting it once moved.