The TLDR describes your method accurately, though. You do store your OTP secrets in a password store.
That said, the significance of using two separate password stores isn't clear to me. Under what threat model is that supposed to be an improvement over a single password store? Basically, your idea is that passwords are less essential than OTP secrets, so you take less care keeping them safe. However I think it'd make more sense to just apply proper protection for all secrets.
That said, the significance of using two separate password stores isn't clear to me. Under what threat model is that supposed to be an improvement over a single password store? Basically, your idea is that passwords are less essential than OTP secrets, so you take less care keeping them safe. However I think it'd make more sense to just apply proper protection for all secrets.