So many good suggestions, I am overjoyed as a SS enjoyer. Quoting them all would make the posts 2m long.

Everyone asks what the historian can say but no one asks how is the historian. 
Mmmmm.
More details or conflicting history about the terraforming for later colonisation of Penelope etc? Why did it stop, what failed, who had his hands in it? Was it "just" the collapse?
Maybe rumours about a moving nexus, more lore about the gates, stuff about slipstreams, domain megastructures, large scale conflicts the domain fought?
Pirate lore about factions, infighting, history, also more history of the stations and what factions have their dirty claws in it all?
Thoughts, speculations on a possible reintegration with the domain and happenings IF the gates come back online?
More leaks about Tri-Tac stuff, especially weapons, ships and Redacted and tech "sharing" with other factions. Some abominable lore about P-space shenanigans, Ludd forbid.
What happens to the mind and body after 500 years of Cryo sleep? From the shock that everything changed, from language to being far away from "home", family members and friends are gone to potentially damaged tissues and memory loss. What about gene altered people, people not used to "current standard gravity", people able or not able to perceive certain wavelengths of light etc, differences between Cryo tech and the resulting problems and advantages. Cryo rebellion (factions) when?

More history about some complicated, multi sided, multi faceted, multi faction wars with interesting results? Be it in the sector or older Domain history. Maybe some name drops for propaganda slogans or "brands" of resistance movements of future, current and old political ideologies within the Domain (probably without taking a stance, but maybe the historian has preferences)?
Shield technology, where are our modulators? What about using shield generators and drives us bombs? What other von Neumann shenanigans are lurking in the Galaxy? What about star drives and rogue planets with outposts? What parts of the galaxy (and outside) did the domain explore, what missions were sent?
How are the "makeshift" stations of the pirates and Pathers made?
What about exotic planetary constellations like 2 similar planets orbiting one point between them, natural phenomenon, did the Domain cause that? What celestial magic &%$! did the domain do? Probably too secret or maybe too big to hide?
Power generation in colonies? What about hydroponics and gene/seed databases, where are those (hidden)? What was lost? Kale? Are we mostly on tastepaste.TM?
E: Jangalas etc. weather, also related variations in toxicity. Trying to fight toxic organisms and waste in colonies with "fire" and everything getting worse.

My, huge apex predators here? Let's set our own free, suddenly they take over and become immune to our counter measures.
E2: Lore about longer term Abiogensis, mutation, guided evolution projects? And more unethical TT stuff.
E3: Who knows whom? How came that to be? Potential conspiracy fodder incoming.

Maybe the lead engineer who was responsible for X (battlegroup modifications, colonial items of company Y) was somewhere in cryo sleep in the sector... With a special long term mission or goal. Who did that person met? What happend after that?
E4: Medical tech? Artifical blood? Futuristic oxygen generation/extraction methods? Who owns that stuff, what was lost? Who has access? Apparently only the rich/upper echelons? Also more Persean league and lower level politics (there), please.

How come pirates can easily sell local production slots? Sus.
E5: How different are the customs from one one end of the core to another? Almost alien? Almost the same? What implications does it have for people who actually can afford to move from one end to another (for whatever reason they'd actually do that). Is the culture mostly stuck, degrading since the collapse? Is and was the Domain so rigid that it stifled cultural, maybe even the evolution of language?
Conditions on planets and how they affect the people, see also Cardamine in Freelancer.

E6: We can see how fast a base burn travel across hyper space is, but how long does the trip last for a civilian or (small) trade convoy? How dangerous are the pirates or can they be bribed? Might there be occasionally a huuuuge convoy from place x to y so that pirate attacks are a non issue if one can offord to wait? Consisting of different factions (not at war?) and indies? Duration? Danger? Comfort? How tightly controlled are the faction convoys by their own faction? Are Hege convoys mostly people working directly under the Hegemony or do they mostly consist of people who are working for companies which operate in Hege space? How much control does the Hegemony even have over their local businesses? Is most stuff directly (or majority) owned by the Hegemony there?
E7: Communes and mechanization of farming settlements in Luddic space and historical growth of them including details about the population and family structures and their values, maybe a snippet of a published biography (of some pre or mid or after Ludd pioneer) which went viral. Other historical events, reactions to catastrophes, is there a unified government or did everyone come together to help? Did some of that influence Ludd? More sectarian differences, also customs on different areas, not just in Luddic controlled space. What about a historic photo and related rumours of the fuel dictator and a potential spouse, with some major twist related to our new quest?
Maybe the person from the photo is still alive (for reasons, cryo sleep? For what reason, can we meet that person later?).
E8: Inspired by the post below me: Hacking and "Cyberpunk" culture, Gargoyle cannot be the only one who is like that, right? Or maybe he is. AIs and "subroutines" for hacking, what can be bought, how is the market, trading of known exploits, how are AI/TT/Pirates etc. involved, possible counter measures, very smol tie in to some of the fake radar signal/hyperspace stuff. Why does my TT pad flicker? Sus.
Also AI/forge/Domain structure/human hacking, maybe some history or a major historical incident or accident.