And it would be pretty weird if our heroes only sailed around doing cocktail parties, archaeological digs and courtesy calls to their android friends while their non-android friends were dying at the battlefronts. They didn't even mention the war in a single bit of dialogue! What are they, cowardly soldiers or heroically pacifist or people from some sort of a parallel universe or what?
Not to mention that the diplomats would have one hell of a time trying to speak with the Dominion if the war was still on. The last time diplomacy was attempted, in "Statistical Probabilities", it turned out that the enemy didn't really believe in it.
And while I can see Starfleet working with their former enemies, I cannot see them working with their current ones. It was no secret that the Son'a were on the Dominion side when this was mentioned in DS9. Rua'fo would have been shot at sight if he tried to approach the UFP before the war was over...
While the Son'a were producing Ketracel White for the Dominion, I suspect they weren't totally affiliated with the Dominion at this point. More likely, they'd signed some sort of wishy-washy non-aggression pact, much like the Romulans did. It was only sometime after the events of Insurrection that Son'a-Federation relations soured and the Son'a became more solidly on the Dominion side.
It was generally pretty sucky that there's so little evidence of the Enterprise, or any other sovereign-class ship for that matter, serving in the Dominion War. Rather than this glorified TV episode, I wish that Star Trek IX had been a Dominion War story.
Do they not give a stardate at all during Insurrection?
No. IIRC, Insurrection is the only movie that doesn't give a stardate.
In my personal timeline, Insurrection is set in the gap between the 6th & 7th seasons of DS9. This is one of the many random, detached duty assignments that Worf took during the period where he was trying to get over Jadzia's death.