A really cool outcome of statistical mechanics and thermodynamics is that what you suggest is impossible. The dyson sphere can be as amazing as you want, using every single trickery permitted by physics, but at some point it will enter thermal equilibrium with its host start (or pipe that heat somewhere else where you would still be able to see its thermal radiation). Inherently, if they are optimized to be good absorbers, they will have to also be thermal emitters. There is no such thing as "recycle all spectrum".
Tangentially related to the fact that a "perfectly black body", i.e. a perfect absorber, is also the perfect emitter of thermal radiation of its own.
Couldn’t one build a dyson sphere around a blackhole? Wouldn’t the blackhole have properties of a Bose–Einstein condensate given the matter at the center cannot vibrate?
It would be the coldest temperature possible. Heat moves downhill, you deposit heat into a singularity and have a shell around it.
That aside, at even a scale of a single dyson sphere, something tells me when a civilization has the power to bend spacetime, the rules of possibilities begin to change. I think it is unwise to operate with so much certainty in the face of possibilities.
And the Milky way would have to be un-dyson sphered, because if it were, we would be able to notice these spheres close up. e.g. if dark matter is 5x regular matter, we would expect there to be 5 Dyson spheres of stars the size of the alpha centauri system all within 4ly of Earth. This would be easy to detect through occlusion. Also, gravitational interactions between sphered stars and unsphered stars would be easily observable in our own galaxy. So for this to work, at minimum, the whole observable universe must by Dyson sphered, except for our own galaxy.
There is an advantage to arranging dyson spheres closer together in order to reduce latency between nodes.
If your dyson spheres were optimized enough, could absorb all known spectrums and recycle them. Wouldn’t that appear completely dark save for gravity?
I mean, isn’t it possible entire galaxies have been converted in this way? Seems like it could be a much simpler explanation within the confines of current understanding.
But I’m sure this has been thought about and accounted for.