Really, the Section's agenda would imply that the positive
things we see onscreen are their doing, and the negative ones are what the Section was established to fight against...
S31 agents would probably have been hard at work to undermine
the coup of ST6:TUC, for example, as they were primarily out to protect Federation integrity (at least insofar as the Federation's public image goes). They might have liked the idea of a decisive war with Klingons, but they would definitely have wanted it to take place in a way that left the Feds smelling like a whole forest of roses.