Nope, TOTP is vulnerable to phishing just the same.
Ordinary users think the fact your phishing site accepted their TOTP code is actually reassuring. After all, if you were a fake site, how would you have known that was the correct TOTP code? So this must be the real site.
The only benefit TOTP has over passwords is that an attacker needs to use it immediately, but they can fully automate that process so this only very slightly raises the barrier to entry, a smart but bored teenager can definitely do it, or just anybody who can Google for the tools.
Worse, TOTP involves a shared secret, so bad guys can steal it without you knowing. They probably won't steal it from your bank because the bank has at least some attempt at security, but a lot of other businesses you deal with aren't making much effort, and so your TOTP secret (not just the temporal codes) can be stolen, whereupon all users of that site relying on TOTP are 100% screwed.
Notice that WebAuthn still isn't damaged if you steal the auth data, Google could literally publish the WebAuthn authentication details (public key and identifier) for their employees on a site or paint them on a huge mural or something and not even make a material difference to their security - which is why this Memo says to do WebAuthn.