It seems like it's been different things at at different times:
United Earth: data brokers with embedded assets. Probably operated more like The Pond than the CIA.
UFP-Klingon War era: Section 31 has grown to the point is has its own uniforms, badged officers, even fleets of ships, culminating in the disasters of the Control crisis.
(During similar time frame in the Kelvin timeline, Sec31 likewise is enlarged enough to command ships and at least one ship construction facility)
Post-Control: Section31 Becomes a sad parody of itself with a series of screw-ups, at least once managed by another screw up, former galactic Empress.
Khan/Genesis Incident and Follow Up: Section31 so diminished by this point they appear to not even be involved. leaving the cleanup of the incident to Starfleet security, and assumedly, Starfleet Intel.
by the Dominion War: far more secretive with plausible deniability, Section 31 operates more like it initially did in the United Earth period.
United Earth: data brokers with embedded assets. Probably operated more like The Pond than the CIA.
UFP-Klingon War era: Section 31 has grown to the point is has its own uniforms, badged officers, even fleets of ships, culminating in the disasters of the Control crisis.
(During similar time frame in the Kelvin timeline, Sec31 likewise is enlarged enough to command ships and at least one ship construction facility)
Post-Control: Section31 Becomes a sad parody of itself with a series of screw-ups, at least once managed by another screw up, former galactic Empress.
Khan/Genesis Incident and Follow Up: Section31 so diminished by this point they appear to not even be involved. leaving the cleanup of the incident to Starfleet security, and assumedly, Starfleet Intel.
by the Dominion War: far more secretive with plausible deniability, Section 31 operates more like it initially did in the United Earth period.