Setting Jam: Hyperbolic Trajectory

[PTTG]

I've been really hankering for a hard-ish science fiction setting. What I mean by that is that it avoids the obvious pitfalls of softer sci-fi, and adopts the aesthetics of real diamond-hard "speculative engineering," but is ok making assumptions where convenient to allow the story to proceed. The Expanse is a great example, as is much of The Andy Weir ouvre. For visualization, see SAVAGES, The Lunar War, and Mare Ignis. Transhuman space is cool, but we're going back to the drawing board and taking a fresh look at everything, and probably looking at an earlier time period.

If you have the same craving, please join in! Ask and answer questions, and please quote. We're going by SCP rules: there's no canon but try to yes-and previous ideas.

Some non-binding general thoughts before we begin: in keeping with the themes, there's no FTL, artificial gravity, force fields, or handheld laser pistols. More recently discredited tropes are hyper-performance rockets (no acceleration above 2G is likely), hyper intelligent AI (intelligence explosion takes time and has limits), and magical nanotech (waste heat and energy storage). Any exceptions should have some rationalization, and ideally point to major adventure seeds. And finally, I would like to avoid individual modern nations having an identity in the game. Ideological factions is great, but nations should exist in the background to avoid casting any players as the bad guys.

Ok, that all done, here's some starting questions:

Where and when is this set? What are the borders of the known?
What's an important group in the game?
What's a good character background?
Why might 2-5 people find themselves in control of a spacecraft?
What's a rumor someone might hear?
What's something common now that's rare in-universe?
What's the solution to the Fermi Paradox, or is it as mysterious as it is now?
Who is a powerful individual NPC?