Section 31 is not comparable to the Tal Shiar or Obsidian Order, not just because they are unaccountable but because they don't exist, they're the Federation's Illuminati, an urban legend, a conspiracy. Probably started out in the dark corner of the mess at Starfleet Headquarters with a couple of old admirals chatting about how dangerous the galaxy really is for a peaceful organisation conducting missions of exploration and science. One of them then jokes that extraordinary measures could be taken all the time under Article 14, Section 31 of the Starfleet Charter since the are constantly under extreme threat.
A few days later one of the admirals needs some thing less than moral done but for the survival of the Federation, calls up the guy who made the joke, asking to pull some strings all under the vague terms of Section 31.
So a network slowly builds, never official, just friends in the right place, recruiting those Starfleet officers willing to 'walk with the devil in the pale moonlight' for, at least in their minds, the greater good.
So who controls Section 31, hands out the orders?
Perhaps no one. If their objective is simply protecting the Federation, sometimes from itself, maybe an individual member just summons the network and it's resources just by reaching out. If the plan has traction it moves, if not nothing. No grand plan just defense by what ever means.
But that's just like my opinion, man.
