Some password managers like 1Password can do the two-factor stuff for you, so you don't have to pull out your phone. On the fully supported pages it'll just autofill your username, main password, and one-time password.
Just as a reminder. If you save the 2FA token in the same password database as the actual password of the website you effectively neutralized 2FA or at the very least weakened it.
If you store your password in a password manager, is it accurate to still frame it as 'something you know'? Or is it just another 'something you have'?