> From my (limited) understanding, entangled particles don’t remain entangled if they are far apart or if something else “touches” one of them, which is not at all how it is explained in the article.

Entanglement is not an all-or-nothing deal. Entanglement is correlation + superposition. If two particles are in a 'large' superposition (they are simultaneously in multiple states which are very distinct from each other), and their states are highly correlated with each other, they are very entangled. This is what typical spin entangled states look like. One particle is 50% spin up and 50% spin down, the other is 50% up and down, and they are maximally correlated - they will always be spinning in opposite directions. When you observe one particle, you precisely know the state of the other.

However, it's also possible to have very weak entanglement. For example if one particle is in a location superposition, and it interacts with another particle from a distance, their trajectories are now entangled. But this entanglement can be arbitrarily weak. If you observe the location of one particle, you gain a tiny amount of information of the other one - if you thought the location would be clustered around some target, you know that cluster might have shifted a little bit. But it doesn't particularly help you narrow down the location.

There's no strict line between weak entanglement and no entanglement. Extremely weak entanglement still exists in macroscopic interactions. Our classical world arises from continuous weak entanglement of the environment correlating everything's state, so we don't see any disconnected parts of the world existing in large superpositions.

That's what the skeptics are saying. The tardigrade is entangled with the qubit in a very weak sense. If you had a godlike view that could measure the exact quantum state of every particle in the tardigrade's body, you would notice a very slight correlation between them and the state of the qubit. The tardigrades are not in a clean set of two possible states that exactly correspond to the qubit, they are in the same multitude of microstates that continually interact with surrounding objects and some probabilities of those microstates have shifted around just a little bit.

There have been experiments that do actually entangle macroscopic objects, e.g. large mechanical oscillators. The 'Results' section is the most informative - not only does there have to be interaction with some microscopic entangled states, but the states of the oscillators should also be highly correlated, and the statistical properties have to demonstrate that they are in fact in a non-classical superposition. The tardigrade experiment did not do this clear work.