We've actually hinted at a Questor/Data connection in the Trek novels, insofar as we can get away with it. Jeffrey Lang's TNG novel
Immortal Coil revealed that Flint from "Requiem for Methuselah" had mentored Noonien Soong under the alias Emil Vaslovik, which could be taken as implying that Flint chose the alias in honor of Questor's creator. When I featured Flint in my
Enterprise: Rise of the Federation novels, I had him doing android research with a substance called bionic plasma (from
Questor), which I suggested was the same thing as
Voyager's bioneural circuitry. I also had Flint (who was using his Abramson alias at the time) state that he had met an android before. My assumption is that Flint learned robotics from Vaslovik and/or Questor, then passed along his knowledge to Ira Graves and Soong.
As for
Genesis II/Planet Earth, I like to assume that's the alternate timeline where Gary Seven failed to prevent the proliferation of orbital nukes. The increased peril led to the development of the underground defense complexes seen in G2, and when the Eugenics Wars broke out in the '90s, they escalated into the full nuclear apocalypse in G2/PE's backstory. In this theory, the mutant subspecies seen in G2/PE are actually descended from Augment experiments rather than being the result of radiation as the movies assumed.
I don't try to reconcile
Spectre with the Trek multiverse, though, since it's straight-up supernatural horror. If I wanted, I could handwave the supernatural entities there as aliens indistinguishable from magic, a la "Catspaw" or Megas-tu, but that would go against Roddenberry's goal for
Spectre to be genuinely supernatural, rather than being the kind of thing where there turns out to be a rational explanation. I suppose there's no reason
The Lieutenant couldn't potentially be in the Trek universe, though I've never seen it.
That does sound at least possible — and certainly it’s more inspiring to have rationalistic humans rebuild the world than to have it only happen because of the Vulcans. Oh well.
Well, it wasn't
only because of the Vulcans. What they said in
First Contact was, "You get to make first contact with an alien race, and after you do, everything begins to change... It unites humanity in a way no one ever thought possible when they realise they're not alone in the universe." So the Vulcans were only a catalyst, allowing humans to see themselves as one species and thus come together to rebuild their own world. It wasn't about the Vulcans specifically, just about the fact of first contact with aliens. After all,
Enterprise made clear that the Vulcans had declined to help humanity advance too much because they feared our potential. So it follows that humanity had to do most of the work itself.