Or say you have a FIDO 2 Security Key from Yubico. As well as the features of the cheaper FIDO 1 Security Key products, this has a PIN verifier. The PIN is something you know, while the Security Key itself is something you have, so that's two factors, once again the UV bitflag is signed.
It's simpler, it's easier, it's more secure. And yet, right now I bet an HN reader is implementing yet another shitty SMS-as-2FA hack and we're still in a thread about remote authenticating with passwords - an idea that was already terrible in the 1970s.
If your threat model is "People fully compromised my phone" then you should definitely not rely on the phone in the face of that.
Recommended if storing 2FA codes in a password manager is to use 2FA for the password manager that isn't stored in the password manager. Off the top of my head, that doesn't seem to really open up any additional risks over storing 2FA passwords outside of the password manager.
Personally, it's a matter of practicality - I use my phone for personal 2FA codes, but don't have a work-provided phone and am not going to use my personal phone for work purposes - and as many services now require 2FA, it's easiest to store those 2FA codes in my work-provided password manager.
This should help alleviate some of the worst password manager risks.