Headcanon: Section 31 was just a bunch of Starfleet Intelligence agents getting frustrated and going rogue, and is not a official huge organization. Starfleet Intelligence IS capable, but limited, by their laws and ethics, but they do have, say, Black Fleets, Black Budgets, and far reaching connections equal to anything the Klingons or Romulans can do.
Section 31 thereof does reappear repeatedly, but discontinuous, to each other, and mostly in times of crisis - like the Dominion War, and even then they were of questionable use. Because going rogue is not actually effective, no matter how badbutt they think they are.
Eventually Starfleet Intelligence reintegrated and dissolved the rogue agents. One or two literally.
I don't mind people going rogue or splitting off at times, especially for a fictional work. In our democracy in the states, the CIA has gone 'rogue' with Project MKULTRA, so much so that the CIA director Helms went against the congressional committees and was rightfully trashed for it. The Counterintelligence Corps in ww2 ignored Roosevelt and Truman's direct orders, kept lists, watched domestic protests after the war above 20 people, and had to be curtailed. Et al, et al.
But I hate that Section 31 is so inflated to be something so big and crucial, and feeds into the 'hard men do hard things so soft men can enjoy soft things' trap/undermining democracy via doing undemocratic thing.
Even if you believe in that, that is not the spirit of Trek and its Federation, which to me is hard men doing hard things to be soft men and enjoy soft things - the frontier captains, the diplomats, the engineers, pushing science, engineering, diplomacy and conflict for a better ideal. It doesn't need a rogue org behind the scenes, we're already following the brick-layers on screen