That sentient being better aim his radio beacon directly at Earth. If it was an omnidirectional broadcast it would need immense amounts of power to still be above the noise floor by the time it got to us. Omni signal strength drops with the square of the distance.
For example, if you traveled away from Earth carrying our best radio detection gear, you could not detect Earth’s radio emissions after you got out to about a light year. The Voyager probes are already -308 DB down, and we can only communicate with them because they point a directional dish at our huge directional dishes which are pointed straight at them. If we were looking for a random probe in a random direction, we would never hear them.
IMO, we may never hear radio signals from other civilizations, regardless of how many of them are out there. Using stars as amplifiers for light signals seems more likely. Another possibility might be communications through ‘seeding’ stars with rare elements in quantities that encode information to be read through spectroscopy. Low bandwidth, but the signal could be ‘read’ from large portions of the galaxy so long as the light is being blocked in their direction.
Maybe when we build a scope large enough to detect small enough changes in star brightness we’ll find all sorts of communications going on by modulated starlight. We can currently spot ‘transits’ of earth-sized planets around fairly near red dwarfs. How big a telescope would we need to be able to see a giant set of louvers in space opening and closing in front ofma star?
But the fact that we haven’t heard any radio signals yet is not really evidence of anything, given how bloody hard it is to send any kind of EM signal interstellar distances. Laser communications, maybe. Some other form of very tight beam signal, maybe. General broadcasts? Highly unlikely.