this issue is now resolved: I found this article:
https://support.displaylink.com/knowledgebase/articles/1188004-macos-10-13-or-10-14-video-functionality-not-enab
And indeed - the DisplayLink driver was disabled - although - I did not get any prompt during the installation. I removed the driver, and then the "Allow DisplayLink...." appeared in the security preferences, then I reinstalled the driver and on the next boot removed and re-inserted the DisplayPort cable, and it started working.