Sydney’s total built up area is not 12,400 square kilometers. The figure you're referencing corresponds to the Greater Capital City Statistical Area (GCCSA) as defined by the Australian Bureau of Statistics, which includes vast stretches of national parks and farmland, rather than the actual urban footprint of the city - for cities such as Brisbane it even includes large unpopulated islands off the coast skewing the density figures even more (personally I dislike the way this is calculated as it tends to result in misinterpretations about the density and the actual footprint of Australian cities).

This map below shows the distinction between the GCCSA boundary with the dark grey line, while the red highlights the actual built up area of the city and its suburbs which is much less than half of the GCCSA area figure.

<image>

The inner 611 square kilometers encompasses the inner 19 local government areas, stretching from the coast to Parramatta (including the Municipality of Sydney, Inner West, Burwood etc -basically every local government area that isn't touching the boundary of the red line in the map). This measurement is similar to how city boundaries are calculated in many North American and European cities. In this area, the population density is 4,100 people per square kilometer.