It's far from certain that the Discovery and the Glenn were built around the spore drive experiment. Rather more probably, the eccentric scientists were given surplus ships to play with, along with half a dozen other eccentric scientists who were running all those other experiments Saru proudly said the ship was capable of. Eccentric scientists just deal with high energies, so they needed ships with spinning lightning rods.
The project is still immensely classified as of 2257 - fewer people know of it than there are folks in the know about US bioweapon programs of, say, WWII or Vietnam era. Keeping it under the lid is not the problem. Finding the motivation to keep it under the lid is; and if the motivation gets explicated in the show, our next worry is whether this really will keep people from writing memoirs half a century after the fact, meaning somebody (hero, villain, other) will commit himself to rediscovery.
Which is why it would be preferable for the project to remain a secret and be a failure. Thus, nobody would read about that desperate hour when scientists were installing cats inside bombs to serve as guidance systems and get ugly ideas: not only would the Men in Black Badges be extra careful about eliminating witnesses, but the idea would not attract anybody any longer. But we need a failure that doesn't let the spore drive serve as a means of mass destruction or bank heists or making your noisy neighbor suffer - a failure that makes people turn away from the drive for good.
As for Genesis, quite possibly everybody has one in his kitchen in the 24th century. The tech was simply perfected and compacted and now serves man at the push of a button. Problems of galactic food shortage solved at much less fuss and cost than the creating of breadbasket planets would entail.
Timo Saloniemi