This "Sirius Sector" I agree does not mean a galaxy, which does indeed have hundreds of billions of stars. I think more like a local cluster of stars, kind of like the Pleides:
Problem is, Sirius (Alpha Canis Majoris) is actually part of the local cluster around the star known as Sol.. It's a shame those programmers went through so much trouble to include all sorts of astronomical data in the game such as the spectral class and luminosity of the stars and all sorts of different celestial bodies only to choose the wrong background to set the game in.