> I’m not sure how the tardigrade could be entangled. 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.

There is no known or conjectured limit on the distance of entangled particles. We have created and maintained entanglement over kilometers (newest result between two atoms on Earth was 50km; photons in space was 1200km). You can also perfectly well "touch" them; if A, B are entangled, you can entangle B with C without it loosing the entanglement with A. It is unknown what the limit for the amount of entangled atoms is, or if there even is one.

Hence it is potentially possible to entangle a tardigrade. The issue here is the question if that actually happened and many disagree. But the discussion is still up and should be left to those that actually work on such things on a daily basis.