It should be a conspiracy of like-minded individuals that exists parasitically within Starfleet, not an official (or an unofficial official agency).
In fairness, Sloan said they were a branch of Starfleet Intelligence with an official designation in his very first appearance on DS9, and nothing that came after that really contradicted him (other than his obvious lies in “Inter Arma Enim Silent Leges”).
Whatever liberties have been taken since then, that wasn’t one of them.