Not so:

They found that airport radar systems, which sweep the skies for airplanes, send out a combined radio signal of 2×1015 watts. That’s enough for telescopes comparable to the Green Bank Telescope in West Virginia to pick up as far as 200 light-years away. [0]

200 ly is about 100k stars

[0]: https://earthsky.org/space/airport-radar-could-signal-earth-...

Huh - very interesting! Now I am going to have to calculate this for myself!

Seems that (r_d/(theta_e z))^2Pt_p ~ 100 hv (~100 photons at 3 GHz; a single 3GHz photon is about 2e-24 J) I'll drop this to 1 photon below.

Where

r_d = detector radius,

theta_e = diffraction angle of source,

z is detection distance,

P = 2e15 W (peak power of source, according to article) and t_p is pulse duration (say, ~5e-9 s).

Now theta_e ~ wavelength/(emitter radius), let's say the detector radius r_d ~ emitter radius = r ~ 3 meters for simplicity. Lambda = l = 3e8/3e9 m ~ 0.1 m) E_p = Pt_p ~ 2e155e-9 ~ 1e7 J (!)

(r^2/l)^2(1e7 J)/(1002e-24 J) = z^2, so z ~ \sqrt(100 m*(1e29)) ~ 3e15 m

But one light year is ~1e15 m. If I assume they have single-photon sensitivity in the microwave regime, then I can boost this result to ~30 ly. So about 1 order of magnitude less than their paper, but that is for a single photon of a single radar pulse. If you sum over many pulses from all the different radars that could be emitting over the integration time then, yeah, I guess 200 ly isn't ridiculous.

Curious what the cosmic microwave background is compared to this though...

The signals will get there in up to 200 years from now.