> In this case the device is just your brain
And that makes it a password (i.e. the primary factor, not a second factor). The whole point of a second factor is that it's not trivially cloneable (hence why, for example, SMS is a poor form of 2FA in the presence of widespread SIM cloning attacks).
No, the defining characteristic of a password is also how it is used: it is communicated in the clear to the verifier, thus revealing it to eavesdroppers. It is highly non-trivial to clone the knowledge in someone's brain if they never openly communicate the mTOTP secret but only do the computations in their head.