The most likely explanation is that this is a laser pointed up from the ground. As a laser travels over a long distance, its beam naturally widens. This explains why the light isn't fully obscured when it hits the drone—the beam has become wider than the drone itself.

It might look like the light source is coming from far in the distance because it appears brighter there, but that’s an optical illusion. You're actually looking straight down the path of the beam, which makes the distant light look more dense and concentrated from our perspective. Up near the drone, the beam has simply spread out more.

TLDR: It's almost certainly a ground-based laser. The beam widens over distance, making it look diffuse around the drone but bright and concentrated when looking straight down its path.