Well, no - if we assume server password db leak includes leaking totp shared secret...

But that is also why I'm not overly concerned by the bitwarden model: in client compromise (ie phone), attacker gets both password and totp secret. But so too in many examples of server compromise.

Seperate totp app doesn't really mitigate any risk factors - but a seperate hw token/device do.

You could have 2fa only on phone, password manager only on desktop - but then logging in anywhere on your phone is inconvenient.

Then again: "Security is not a convenience".