The Best of Trek mostly were interviews with actors, actress, producers, director and other that made Star Trek, as well as short stories.
Never the less, they took those fan created stories and put them in Star Trek The Final Frontier, Star Trek Enterprise, Star Discovery and Star Trek Strange New World.
It would be up to the creators and writers of Star Trek Strange New Worlds if they wanted to bring in Spock haft sister. Spock only would have seen her only when his parents, Sarek and Amanda had business on Earth. Which means he knows little about her.
There was
one interview each with Walter Koenig and Grace Lee Whitney in the first
Best of Trek volume and coverage of a convention speech by George Takei elsewhere in that same volume. IIRC, there was also an essay by Russell Bates, who wrote "How Sharper Than a Serpent's Tooth" for TAS, but I think that he had a recurring column running under the title of "99 Character Universe" in the magazine format zine, TREK.
I also think Bates' collaborator, David Wise, was quoted in an essay in a later volume.
The essays in the Best of Trek collections generally did not include short stories. They did include parodies from time to time, usually written by Kiel Stuart. If you push your definition, I guess that you
could include the speculative history in BoT vol. 2 of the Eugenics Wars told in chronological timeline form which matched very little that was told onscreen and was spun whole cloth from the fanwriter's imagination, another speculative biographical sketch of Jim Kirk (which I quite liked at the time), and another speculative future history of the Fall of the Federation.
After Volume Two, those kinds of more immersive fictional speculative articles mostly faded away, to be replaced by the types of amateur literary criticism, personal essays, and speculative nonfiction of the type FredH describes. [Volumes One, Two, Three, and Six were my favorite collections of those books, BTW. My copies of the books still exist after three cross-country moves, but they're long buried in boxes in my garage and largely inaccessible at the moment.]
But, again, I have no memories of any of those essays postulating a backstory for Number One involving genetically engineered augments, nor one involving Amanda's putative first husband and a daughter named Elisabeth. [I will grant the possibility that the latter may exist, but not the former.]
You're overselling the importance of an unlicensed collection of fan essays and claiming that they had more legitimacy and influence on modern Trek than the evidence suggests.