Even without using EM to communicate, and assuming we don't need intercontinental radars [1] anymore, a lot of our regular activities do emit EM. What we find weird is that we only see natural EM sources. If a civilization were to reach 2 or even 1 on the Kardashev scale, we ought to see some non-natural emissions.

Of course there are a lot of assumptions there, and lots of hypothesis to explain it a way, but that's the crux of the Fermi paradox: there is something to explain away

[1] https://en.wikipedia.org/wiki/Duga_radar