You could explain away the discrepancy by saying that the 45 billion number is the number of permanent residents. As the seat of a galactic empire it would likely host representatives and their staff and families from tens of thousands of worlds, would probably be a hub of interstellar trade with many merchants and the crew of their ships staying for weeks at a time, a major tourist and religious hub with billions of visitors and pilgrims, countless numbers of galactic citizens would also make the journey to petition the emperor for various things. The list could go on for a mile and could result in a much larger effective population at any one time.

> It has a population of 45 billion, and a surface area of approx. 40% that of Earth.

I think he retconned this up a bit in later stories, after people had pointed out the problem. But yeah, it's a weirdly common problem in science fiction; for whatever reason few authors bothered to check the density of existing cities before declaring a weirdly sparse world-city.

It’s hard to take making sense of population numbers with the use of fictional material.