It's a bit of a niche within your target domain, but GURPS Traveller Nobles is a really solid sourcebook.
Further into special interest areas are some other GURPS Traveller titles, such as Far Trader (economics, with at least one professional economist as a co-author) and Starports (about the visitor experience of a starport, not just mundane stuff like construction details).
I would guess that the recent stuff by Marc Miller would have a lot of significant details too, but I haven't seen it myself, and my secondhand impression is that the material is not organized as well as it could be.
I think the old Rebellion era sourcebooks would be useful too, because in describing how the fragmented Imperium works, one could piece together a lot about how the unified Imperium functioned. Again, however, that's more a secondhand impression.
There are also the Milieu 0 books, which describe the beginning of the Imperium. I haven't read them closely or recently, but they're interesting reading anyway. Reviews complained about rough editing, but I didn't read them closely enough to notice that.
Short answer: the information is scattered around everywhere, and if you have specific questions you might find answers more easily by asking.