This high level description isn't fundamentally different to how you would actually entangle macroscopic objects. We know how to create microscopic superposition states, and we know that entanglement spreads by interaction. That's the point of the Schroedinger's cat experiment - the decaying atom interacts with the cat through the detector+poison vial, and this interaction entangles them, putting both in a very distinct superposition of vastly different states (decayed and not decayed, and dead and not dead).

The question here is whether the tardigrades were meaningfully entangled with the qubit states by this specific interaction (acting as a dielectric on capacitors within the quantum system). The skeptics say that the interaction of the tardigrades with the actual qubit states is so weak, there is effectively no correlation between the two.

Personally, I was getting Star Trek: Discovery vibes here.