Hello Mario49!
Well, my good Sir... You got it, the "problem," that is, right out the gate! No 'If's,' no 'And's,' no 'But's.' As it turns out, there is a Mac Pro in the office upstairs that determined to load a new MacOS, Big Sur to be precise, some weeks back and also decided to share screens in addition to the printers w/ the MacBook Pro downstairs. That screen share was the source of the banner across the MacBook's screen stating "Your screen is being observed/watched."
So glad the "problem" is not some nefarious "ogre-ware," rather a relatively simple in-house setting on another Mac. Pheww! Problem solved, thanks to you! Your help/assistance is really, REALLY appreciated!
All the best!
iamkappa