SETI began by looking for radio signals that were highly unlikely to be "random" because that fit what we ourselves were using at the time. As we've since discovered, this sort of communication was shortlived lasting just decades.

So what could we observe instead? The answer is Dyson Swarms. These aren't rigid spheres as some seem to think (the original term was "Dyson Sphere" but is largely abandoned because of the confusion). It's merely a collection of orbitals to consume all the energy a star produces. Many (myself included) think this is the inevitable direction of our species.

The only way to get rid of heat in space is to radiate it away. The frequency of the light emitted depends entirely on the temperature of the radiating object. This means a full Dyson Swarm would have a huge infrared signature. That sort of thing we could detect from a very far distance. A whole galaxy of these would be detectable from millions of light years away.