Typically the way these codes are compromised is when they are stored in a non-HSM location like Google drive or transferred somehow. Then again, if you are just trying to keep people out of your Facebook account it's not a big deal. But if you are trying to keep people from financial accounts I wouldn't recommend transferring TOTP keys. Instead using a backup method like a printed out one time use sheet would be better.

Unfortunately most such websites use KBA or Text based authentication as a backup for TOTP so you may as well just stick it in Google drive.