In the Copenhagen interpretation, there is a difference between measuring a system and entangling with it. There exists a unitary that entangles you with the cat, just like there exists a unitary that entangles the cat with the quantum device. By definition, unitary evolution is not a measurement in the Copenhagen interpretation.

> Showing collapse happened is really tricky because of decoherence. Similar to unmixing coffee and milk.

Unmixing would show the lack of collapse (in the specific case), though? To show collapse you'd need somehow experimentally prove that it is impossible to unmix. And to falsify collapse, you'd need to somehow experimentally prove that it is always possible to unmix. And if we go with your analogy, would you say the coffee with milk hasn't forgotten its initial state because it is technically possible to unmix them? Being able to manipulate the whole universe's wavefunction to unentangle particular subsystems is akin to having access to Maxwell's daemon, since decoherence increases entropy.