S31, being a cell based conspiracy, but more than healthy paranoid given what's out there I'm guessing has worked it's way into the Federation communications network and has 'monitors' everywhere that examine data and run threat assessments much like regular SI....except they also tend to work in a coldy pragmatic way when assessing existential threats to the federation (the Borg, The Vedians, The Undine) and will look to prepare by hook (planting an idea in the right admirals or researchers head) or by crook (cultivating the less ethically restrained will bea bit ofa hobby for them) defenses or Weapons intended to eliminate existential threats to the Federation.
They are also probably VERY good at playing the other powers intel services for fools by arranging patsys to be thrown while they run a misdirection campaign to get what they want. The Founder viron was a good example of this. And they are proably pleased with Sisko's "flexability" from the "Pale Moonlight" incident.
S31 should be used very lightly in ST and most char;s should not have a idea what they are dealing with.
Post dominion War Era stuff could be dealing with Jem'Hadar Raiders, Borg incursions, or a lot fo the nasty underbelly of the federation.
but I ramble
A brave little theory, and actually quite coherent for a system of five or seven dimensions -- if only we lived in one.
Academician Prokhor Zakharov, "Now We Are Alone"