FYI, problem solved! But, to be honest, not in the way I expected.
Premise: I got a "healthy" board.
In summary, I plugged the healthy board to the PC, opened MPLAX IDE v5.15 and upload the
starter kit demo code provided by Microchip (https://www.microchip.com/DevelopmentTools/ProductDetails/dm330018
). Everything worked good.
Then I unplugged the healthy board and closed the project on MPLABX. I plugged the faulty board, reopened the project, launched the Refresh Debug Tool Status
procedure (on the Dashboard view), tried to upload it and, against all expectations, success!
Now I can see in the dashboard the correct serial number of the board, which was previously absent.
Frankly, I don't get how this happened, because in all
the previous attempts it failed always without exceptions; hence my guess is that, somehow, the healthy board contributed.