I suppose my question might be more accurately asked as: How would the Federation explain Spock's death and resurrection?
By telling the truth, presumably.
Project Genesis led to the creation of an entire planet and star system, the disappearance of a nebula, and was openly spoken about with a foreign ambassador on the floor of the Federation Council. The cat was out of the bag there; it was already part of the public record. No reason to hide it from there.I don't think they need to explain the "Vulcan Mysticism" part of it, but rather its connections to Project Genesis?
You're assuming that meeting was open to the public.
Why would it be open to the Ambassador of the Klingon Empire to the United Federation of Planets -- a hostile foreign power -- but not the public? It's not like they'd be able to trust the Klingon Ambassador not to leak everything to the press; the Klingons certainly wouldn't obey Federation laws about classified information.