I think it is less secure - for the single case of the password manager being compromised). But I think it is still 2-factor - the thing you know (the password) and the thing you have (proof that you had control of the device (or eco-system) the TOTP seed was created on).
So if you've memorized an uncrackable password for a password manager whose architecture you trust is secure, and use a third party TOTP provider (or a hardware key) for the password manager login I think its as good as using a 3rd party TOTP provider for everything. And a lot more convenient.
So if you've memorized an uncrackable password for a password manager whose architecture you trust is secure, and use a third party TOTP provider (or a hardware key) for the password manager login I think its as good as using a 3rd party TOTP provider for everything. And a lot more convenient.