(Status: Feels close to something right. Make things up and see what sticks.)
(Spoilers for Time to Orbit: Unknown through chapter 42, and minor spoilers for later. Minor spoilers for the 2022 movie Death on the Nile.)
A mystery story breaks up into two parts: Long-running mysteries and small mysteries.
The long-running mysteries represent meaningful questions of interest. They're things like "Linnet Doyle dead, what the fuck?" or "What the fuck is going on with the Courageous?" For whatever reason we care about them. If we don't actually care then it doesn't matter.
(Aside: I like to frame mysteries as "what the fuck?" because it encompasses all the questions you could reasonably ask: who, what, why, when, how. It makes it much more open-ended how you actually follow up on a mystery.)
A small mystery is something you can act on right now to learn more. It's a mystery like, "We can't find the gun Jackie used to shoot Simon, what the fuck?" So: Go look for the gun. Or, "I found this weird dust at the bottom of my chronostasis chamber, what the fuck?" So: Go get a science person to do science on it.
If we think of a mystery story this way, how does the story look? Do we think of the story as being a bunch of branching and merging lines of small mysteries, as a sequence of disjoint small mysteries, or something else? What does it look like to resolve one small mystery and move into another?
Brainstorming on how the small mysteries fit together: Yes, I think they can arise and dissolve in parallel. Sometimes we have multiple small mysteries going simultaneously. Usually that means "we find some clue, and assign some person or computer or machine to extracting more information." Like: That baker sure seemed suspicious. Inspector Lestrade, go interrogate the baker and see what he knows. Or: Go check his alibi, go talk to his neighbor he says he was drinking with and see when he left the bar. That leaves the main investigator (team)—Aspen Greaves, Hercule Poirot, Sherlock Holmes and Watson—to pursue another line. Then whether the line we pursue works out or not there's the potential for Shocking Events to unfold when the other line of inquiry comes back up again.
About shifting between: Either we find something (many clues) or we don't (red herring). Usually in resolving one small mystery we learn a little bit more about who, why, or how, but not enough to answer any of those fully. The evidence we find might exclude some possible whos, whys, or hows. Like: We found the will, and the guy we thought was the prime suspect is actually on it, and that means we no longer have a motive for his doing it. He might still have done it, but if he did do it, it's not because he was left out of the will.
Explicitly: A small mystery when resolved can also overturn what we thought we knew. Many mystery stories have a small mystery like this. We are led to make some assumptions which later turn out false. We draw some conclusions from those that are also to some degree false. We proceed forward on those false assumptions and this sometimes has deadly consequences, as in Death on the Nile. This also happens in Time to Orbit: Unknown. People die because we're assuming the reported revival chance is actually 10%, but in reality it is 0% because those people have compromised cranial ports.
Eventually what we learn in the small mysteries ties together into a conclusion. So far as I've read there is usually some kind of overturn near the end and one or two before that. That's how we resolve the long-running mystery. Depending on whether the long-running mystery is the entire story or a subplot, it could be usefully broken into a line of small mysteries or a branching and merging series of small mysteries. When it's the entire story, it probably branches more and when it's a subplot it is probably more linear because you have more than one and they can tie into or lead into other long-running mysteries. When a long-running mystery constitutes the entire story it has to stand on its own and so I'd its structure generally to be more complicated.