TOTP codes can be phished. Hardware-based 2FA is a different matter, but SMS and TOTP 2FA doesn't fully protect against phishing.
TOTP codes can be phished. Hardware-based 2FA is a different matter, but SMS and TOTP 2FA doesn't fully protect against phishing.
If you get a message indicating your password was invalid, you're probably not going to pay a whole lot of attention to it--even with a password manager, it's a common message to receive on financial sites. Some go out of their way to impede password managers because they think that's a good security practice.
If you get a message indicating the 6-digit code you entered is invalid, that should be a lot more concerning to you, and you should immediately ensure that nobody has logged into your account. If you can hold out for however long the site will accept the code (usually 60 seconds, but some sites have a larger window), you're good.
Of course, none of these "ifs" exist with FIDO2 and U2F, which is what everyone should be using instead. If you're in charge of security for a website, please offer FIDO2 and/or U2F.
I could type the 6-digit code incorrectly just as well as I could type the password incorrectly.
Additionally, some sites might check both the password and the 2FA code simultaneously as a security mechanism to prevent attackers learning if the password is correct.
Additionally, the phishing page could simply redirect the user to the real site. The user is likely already logged in to the real site, so it will appear to the user as if the user just performed a successful login. If the user isn't logged in, it will seem like some type of site glitch, and I've experienced glitches like that myself.
The complex attack you are probably thinking of is sim swapping which is a bit different than phising.
Of course, if you're a high-value target or work for a company that's likely to be targeted by spear-phishing campaigns, you should be using FIDO2. (Don't target U2F, as there are newer, backward-compatible specifications.)