If your account is through Steam, you MUST start the game via the Steam launcher and log in via Steam. You cannot log in using a username and password, and any attempt to do so will result in exactly what you see: a code that will never arrive.
As long as your base game was purchased through Steam, you must log in via Steam.
I'm not completely certain about this next part, but I think the only way to free yourself from the Steam login requirement is if you essentially bought the game again outside of Steam by redeeming a new game code on the account.
(All this also applies to Epic accounts too.)