The entire use case for Authy is the cloud backup and syncing across devices. If you don’t want that, use any of the other free and more open 2FA apps.
Then make it an independent email+password thing, so in case of a leak, something as critical and personal as a phone number doesn't get involved in the stolen data.
(I know the irony of this in particular being Authy, but nevertheless phone numbers should NOT be risked to be exposed anyhow)
