When they say “galactic center” they are describing a mass of stars which is tens of thousands of light years in span, and contains hundreds of billions stars. The vast majority of them are not influenced whatever by the central black hole.
If we are not alone, that mass of stars may contain thousands of technological civilizations. It’s not surprising that we might detect anomalous radio emissions there. Possibly the radio emissions would be a by-product of some energetic activity such as war or FTL transport.
In Isaac Asimov’s Foundation series of novels, the capital of the galaxy was on a planet of a star near the center, where the sky had millions of close stars and it was never ‘night’ as we know it. Eventually, the entire planet was totally encased in a metal shield with artificial lighting to simulate darkness and lightness cycles..............................