How many people know the full details of the Spartan-II program? Conversations between characters in Halo 4 and the comics imply that even regular Spartan IVs and military officers are aware of the truth behind the Spartan-II program (i.e. abducting children).
I think it depends on the particular time in question. It started in 2511. It was revealed to the public in 2547. And halo 4 takes place in 2557. It was top secret for a while. But over the course of almost 50 years, information gets out. The hunt the truth audio digs into some of this I’m pretty sure. Oni definitely tried to hide their secrets. Can only hide for so long though.
People in the military probably know a little bit through rumors and possible first hand accounts. Most civilians probably know very little about the original Spartan IIs. Just stories of their actions and not how they came about. I’m sure ONI holds most of that information as a closely guarded secret, never confirming or denying claims.
it use to be highly top secret, but at some point after the war it was declassified to an extent and so now all of humanity knows the rumors or truth of origins of the Spartan-II program