I've always assumed that the light used for projection on those must be fairly strong.
Mine isn't bright, sometimes I wish it were brighter.
Attached is a photo shot at f3.2, for 3.6 seconds. Hand-held which is why it is blurry. ISO 800 which is why it is grainy. It was pretty much full dark outside when I shot it, so the fact that you can actually see the window shows that it is overexposed. The piece of furniture on the lower left is being lit by light reflected from a street lamp half a block away.
The clock projection actually appears much brighter in the photograph than it does to the eye. A true exposure would show nothing but the projection, but without any other reference to judge by it would be meaningless.
Anyway, you needn't worry about my projection clock lighting up the room. It's barely bright enough to read, and by the time there is enough ambient light to make out the silhouette of the bird feeders, it is invisible. However, I don't know whether other projection clocks are brighter than mine.
tanstaafl.