OK, but a giant parabolic dish is some parochial 20th century Earth tech.
I was imagining some little guys who create a 100 cubic AU grid of omnidirectional sensors, with a sensor every 1000km, all hooked up the mother of all DSPs. I can visualize that system identifying some pretty faint waves vibing in the noise. Am I wrong in thinking that this system could pickup AM radio really far away, easily... and once they got sick of that, even FM?
An AU cubic grid of detectors would inform you where a signal originates from by comparing free space loss over the area of the coverage. IF you could discern a station from static.
In my un-optimized imaginary system, the sensors are very sensitive and dumb, like me. All the difficult work is done by the central DSP-like brain that can identify even the tiniest of waves moving through the grid.
The utility comes from seeing the relative values in the grid... a pattern of tiny changes in some arc, moving through the grid.
Sure, killer triangulation (actually radial measurement?), but also possibly a decent 500 light-year AM tuner?
Imagine your array popped out SHORT-SHORT-SHORT-LONG-LONG-LONG-SHORT-SHORT-SHORT
You just heard a morse code for SOS! The shorts where detected over 100Mhz (FM) +30db for 1 second each and the longs were 3 seconds each on a carrier that sites at +10db. That's amplitude modulation and that looks like intelligence but unless you knew morse code - it wouldn't make any sense.
The further away you get from the source, the more those decibel spikes weaken and will eventually be no different than the noise floor. Your super computer with a billion ears, only hears ~static~.
Try this, imagine instead if there was no free space loss in the electromagnetic field - we'd wouldn't be hearing humming but SCREAMS from all the noise sources from EVERYWHERE as if we were right next to them, forever. It would impossible to decern anything from anywhere. Communication is defined by its distance because signals have differing origins. Sensitivity, or lack there in, is a feature not a failure.
Who's to say a quasar isn't just a lovely time clock for signals encoded in the noise and we haven't figured out what the breakpoint from noise is yet?
Apart from a) quasars are broad-spectrum, not narrow frequencies (at least I assume that is the case), and b) the power required is too large for a civilization to realistically be able to generate. Not to mention that all that power is overkill for intragalactic communication.
But it’s a good sci-fi idea!