I've watched through https://www.youtube.com/watch?v=4Rb7_WdNlZY, the stream showing a "blacked out" St. Peters square. The "blacked out" square still has the street lights and Christmas tree decoration lit up and at some time (around -40 minutes from time of this post) you can see everything brighten up and the square becomes visible. It's easy to see the increased brightness of the already existing light sources, including a car driving over the square at the time of brightness adjustments.
This leads me to think it's most likely an automatic day/night setting for the webcam that failed but I'm not disregarding a targeted video blackout.
That's the same stream I posted and currently show one person standing next to that lilliput police car, two people strolling over the square and a small group of people walking near the columns. Even if all those people were cops it's not outside what I'd expect from an early Sunday morning on St. Peters square. I kind of assume the capitol of Christendom have activities on Sundays that require security staff.