Re: huge background of all the crap spewing out of that big fusion reactor close by
"the Earth actually outshines the sun in that range"
I was sufficiently interested to check this. Solar output is very roughly 1027W, and for a black body at this temperature the amplitude at radio frequencies is about 1/1018 and down. So the Sun is producing maybe a few hundred megawatts over the "radio" spectrum, and very little energy at the long end of that spectrum, and you are quite right.
The next question, which I can't answer, is how much of the energy produced by terrestrial radio stations actually ends up propagated into space. Taking the solar emission of radio waves, a very rough indeed calculation gives me around 10-35W/sq M for the radio spectrum at the distance of Proxima Centauri, with less than 10-37 over the "ordinary" radio spectrum. Given that photons at this frequency range are pretty weak, what sort of detection and resolution could be expected? I know we can identify a comet lander by just three pixels, but we at least had an idea of where it was.