> However if the aliens had a big telescope surely that radius would expand?
I think a more interesting question is how far away could we detect a civilisation equivalent to our own, using our current technology. Otherwise you can assume aliens (or our future selves) with arbitrarily sensitive detection equipment limited only by whether or not the detectors are inside the speed-of-light radius of the emitting civilisation.
IIRC our most powerful transmissions have been from NORAD radars looking for missiles coming over the north pole. In some ways we are now emitting less detectable signals, e.g. with lower power 5G cells and fibre broadband replacing good old radio.
However if the aliens had a big telescope surely that radius would expand?