A partial answer to your question is that there’s a minimum amount of heat necessarily radiated when doing computation, given by the Landauer principle.
It’s not a given that Landauer’s principle is an absolute threshold - the Wikipedia article describes challenges, and there are attempts like Reversible Computing which can potentially work around it.
Furthermore, I also do not think that we will detect dyson spheres, because if a civilisation wishes to hide, they won’t radiate heat uncontrollably by extracting all possible energy, but rather send that energy elsewhere, for example by dumping it into a black hole. But I could be wrong and such a civilisation might care more about energy than remaining undiscovered.
Fully agree that such an advanced civilization will most likely want to hide, and stop any infrared radiation to the largest part.
Reversible computing can not work around it because one simply can not extract information without irreversibly affecting the system. This is a fundamental constraint due to how, in quantum mechanics, once an observer entangles themselves with a system they can never unentangle themselves. I believe that from that single fact one can derive the impossibility of reversible existence.
