You are incorrect. The only factor used there is the key. The password simply decrypts the key to perform the requested authentication. 2FA would be private

You are incorrect. The only factor used there is the key. The password simply decrypts the key to perform the requested authentication. 2FA would be private key (password-protected) and a separate (most likely one time use) password. Something you have (key that you decrypted) and something you know (the one-time password).