We could be looking at a buzz of streetlights and radio signals so dense it's just noise.
Sort of looking at cities from a 100,000 miles up.
It would make sense that they'd prefer a stable stationary system rather then orbiting.
I mean think-about it, if you wanted to build an almost infinite civilization it would end up looking much like a nebula, glowing sort of organic in shape.
The Crab Nebula
Look at something like the Crab Nebula. I'd bet anything that it's a massive space based civilization. Basically a City that's grown beyond a solar system. It's just too fractal and organic looking in nature.
What would a civilization that were to grow to such an extent look like?
Think about what we see from a city from a distance now. With Digital broadcast there is no simple RF broadcasts now.
It would look like broadband noise.
In the optical band it would be a florescent glow of streetlights. Not much different from some of these nebula.
The one tell tail signs would be organic structure and strange spectral envelopes.
London At night
Tokyo At night
We keep looking for Earth like planets, but the odd's of finding a race at our stage is small.
It's far more likely to find one that's millions of years ahead or behind.
Behind will look like just a planet with free oxygen, signs of plant life, that's it.
But ahead, in a million years think about where we could end up.
We could easily overrun not just our planet, or even solar system,but our sun itself and the next several suns in our local galactic neighborhood.
In 100 million years what would we would look at a distance? Much like a nebula with web of colonies.
A massive extrasolar foam covering a large region of space if you think about it. Hollow air filled living and working chambers with trillions of humans and robots like an massive ant farm in space. Like a bread mold spreading out.
We would consume ever piece of solid matter in this way.
Every planet, meteor and asteroid, even find a way to cannibalize stars.
Expanding it's volume in to hollow structure, a honeycomb maze of habitable space. Illuminated, buzzing with communications. Think Borg home world.
I suspect it would look very organic as that would be more efficient then trying to make square structures.
We'd be way past needing the sun's light and heat, instead we'd have countless fission and fusion reactors, and try to extract every last drop of energy from the Matter we're burning for fuel.
That is if you were to carry things about to there extreme limits, it would have to play out like that.
As for ruling it, it wouldn't have some galactic emperors or any single government control structure but most likely a network forming a super intelligent AI of unimaginable intelligence who's sole purpose is to keep expanding and growing as efficiently as possible. More like plants or hive animals have. Bread molds and other colonies do on a small scale now.