So what I was doing was opening Tools->J-Link Settings:
seeing that it already had the correct Serial number, I just clicked 'Save to Project' - and that doesn't add the current Serial number to the Project.
in the Console, it says:
But if I do choose the '...' for 'Host Interface', select the required Serial number, and then do 'Save to Project' - it is, indeed, saved.
in the Console, it says: