If a cloud based password manager is breached and that leads to decryption of the password vault then that password manager is not fit for purpose under any circumstance, whether you store TOTP keys there or not.
So by default we have to approach from a position of trusting encryption, right? MFA in the realm we're talking about here plays no role in encrypting the vault (yes you can use keyfiles or hardware keys as part of the decryption/encryption process), under this context MFA is about authorising access to an account.
So you can go ahead and store your keys in a second vault, but that vault must have as good security as the password one in order to be secure - i.e. it must not be decrypt-able.
So if each of the vaults much not be able to be decrypted in order to be secure there is no reason to use two, as one will be 'good enough'. not decryptable x not decryptable =/ more not decryptable.
What I would say is that there are key accounts that need to be secured with offline physical protection. For me, and I'm guessing this is the point you're making, those would be the password managers MFA.
If you trust your password manager then you only need to secure access to it in order to secure any other keys/passwords stored inside. So you only need to remember a password (something you know) and use a keyfile (something you have) to get access. You can substitute MFA TOTP key here to if you like, but you just have to secure those two things.
If you trust your password manager, you don't need more than that. You obviously have to trust your machine, that's a rather obvious truism I shouldn't have to point out.
So my point is, be realistic about where you store thing and what you store and recognise where the defence in depth is of value.
So if both of those things are true - what does MFA get me?