This is great news, it proves the light source intensity stopped outside my bedroom window the shadows prove it
There's nothing in the video resembling a moving beam. The "search beam" at 11 seconds (starting 7 frames into second #11, in the 7 second video) stays fixed for twelve YouTube video frames, corresponding to 4 frames of the original, and illuminates many parts of the view including some high foliage, the car, and the ground on the right. It's not a very focused "beam." The way it illuminates the foliage and other objects makes it appear to shine horizontally from behind, a little higher than, and to the right of the viewpoint. There are small variations in brightness during the 12 frames (some of it probably video conversion artifact) but the area illuminated doesn't change, so there's no sweeping/searching motion or any other motion of the light source or the direction it's aimed. If you examined only those 12 frames, there's no way you could conclude that anything was moving toward the viewpoint.
Then a single frame later, the illuminated objects all dim out again (though not to as dim as they were before the "search beam" starts) and the foreground "search beam at the window" light casting highlights and shadows on the pots appears instead. No transitional motion in between, of course. We're pretty sure we know the source of that light.
The broad coverage and lack of any motion in the "search beam" over 12 frames makes it seem unlikely for it to have been caused by a person using a flashlight, or light from a moving vehicle at some distance briefly shining past obstructions. (Those would otherwise be very likely possibilities, during a power outage in a populated area.) It looks in every way like it's from another light fixture in or on the house, above and/or behind the viewpoint. So it's probably caused by the same power transient.
That is, the LED light wasn't the only light that flickered on during the power transient. Some other light was on first. The circuitry in mains-powered LED lights often does introduce a delay when turning them on. It's quite plausible that one fixture would be flickering on momentarily just when another, with different circuitry, was already shutting down, after a transient surge of power. There's a bit of coincidence in that (though less than it might appear, once one realizes that the original video frame rate must have been only about 10 frames per second).
I always unplug electronics during power outages, because I know surges and transients in the line can happen. Most of them happen within a few seconds after the power has gone out (can't unplug things that fast, so I have to fall back on the surge protectors), but they can also happen while its coming back on or at any time in between. Like any system in a failure state, there's no guarantee that failed power will remain within its normal specifications.