I believe that functionality is opt-in (or a very prominent opt-out process), but yes I would say you no longer "have" the key, but are turning it into "knowing" a password required to retrieve the key.

Still Zero-Knowledge, but no longer really 2FA.

I still us Authy for a lot of my keys because (1) I have that cloud function off and (2) the UI is better than GA IMHO.