I like to imagine that this is how things would look if we entered a Karadashev type III civilization's light cone:

One day, in a small quadrant of the galaxy, we'd notice starts "shutting off", simply going dark. After a few months, our astonomers would confirm their new model: the amount of stars going dark is increasing. Days later: the rate of increase itself, is increasing. One day we'd wake up, and a small portion of the night sky would be dark. A disk of darkness, right at the brightest part of the galactic plane. By then we would have figured it out of course: most stars in the galaxy were being turned into dyson spheres. They were spreading almost as fast as light, making it look almost instantaneous, even though the process had taken hundreds of thousands of years. In a few thousand years a large portion of our sky would be dark. And after that...