2FA protects two different attacks: 1) Hacker obtaining your password (through phishing, compromise of third party, etc.) 2) _You_ actually being compromised yourself somehow.
It is still effective for the first protection if you store your codes in your password manager, but less for the second. I say less, and not completely, because if your machine is compromised, gaining access to your phone too is only a matter of time. Of course this can be mitigated why proper hardware tokens, but most people aren't using those.
It is still effective for the first protection if you store your codes in your password manager, but less for the second. I say less, and not completely, because if your machine is compromised, gaining access to your phone too is only a matter of time. Of course this can be mitigated why proper hardware tokens, but most people aren't using those.