Thats the final piece. (and you swapped out HD USB cables too on the "bad" HD?).
After swapping cables between the "2 identical WD USB HD", you have (nearly 100% certainty) a bad SATA card as I stated much earlier.
The case being, your other Macs will read/ write to this HD fine, but this one Mac wont. It makes very little logical sense to most (for obvious reasons), but that that one Mac is no longer able to communicate with said HD due to the SATA card.
.......This is why some of us HD 'collectors' call this the "haunted HD syndrome" 😐, where a HD acts utterly illogical and contrary to common sense diagnostics (works fine on ONE Mac but not another)
You have 2 options, offload all data onto another HD that will work on that one Mac, OR crack open the HD case and remove the HD itself and put into another enclosure ($10-15$ ebay).
A SATA card is about the size of a stick of gum, its plugged into the HD with a female USB connection on the other side, it unplugs in 1/2 a second from the HD once you get into the HD casing. Its a (junky) 50 cent part.
If a HD is over 3 months old (most all "bad" HD fail usually before the 3 month mark) and LESS THAN 5 years old and treated very well, ....people that assume a non-working HD is a "bad" HD when in fact the HD is just 100% fine, its just that miserable little circuit card. 😟