That’s not quite right though, there’s the factor you know (password to your vault), and the factor you have (a copy of the encrypted vault).
That would be true for offline vaults, but for services hosted on internet I don't think so. Assuming the victim does not use 2FA on their Bitwarden account, all an attacker needs is the victim's credentials (email and password). Once you present the factor you know, the vault is automatically downloaded from their services.
This is something I hadn't thought until know, but I guess password managers might(?) change the factor type from something you know (the password in your head) to something you have (the vault). At which point, if you have 2FA enabled on other services, you are authenticating with 2 things you have, the vault and your phone.
The only thing this does is replace the authentication mechanism used to unlock the vault, instead of using your master password (something you know), it uses some biometric factor (something you are), although it uses your biometric data, it's still a single factor of authentication
I am not sure I understood you here. What do you mean by "instead of having each service do their own thing"? Each website using their own method of delivering OTPs?
I am not discrediting password managers, they have their uses, as you mention you can have unique, high entropy password on a per service basis. The only thing I am against is the password managers themselves also doubling as OTPs generators (take a look at Bitwarden Authenticator which kinda defeats the purpose of OTPs. From the perspective of OTPs it makes much more sense to use a separate application (Like Google Authenticator or Aegis Authenticator), preferably on a separate device, to generate the OTPs.