...It took quite a while for them to discuss any past conflict, be it Cardassian or Talarian or Romulan or whatever. Wars just aren't popular conversation topics in Starfleet.
Heck, it took them great effort to discuss even an ongoing conflict. The first we hear of the Cardassian War is "The Wounded" where we learn the war was on for all the previous seasons of TNG, with zero mention. Not that TOS would have been much different: Klingon hostility was "unremitting", but the first we hear of this "constant" arch-enemy is when they choose to go for a major offensive, in "Errand of Mercy".
Is the Dominion conflict ongoing or in the past during ST:Insurrection? Given the above, it's impossible to tell. And there's no stardate to help us out there. We do learn that there are diplomatic negotiations with the Dominion in progress, which doesn't sound at all probable during the war ("Statistical Probabilities" would have weaned the Feds out of believing in negotiating, and the Founders grew too fanatical to allow for negotiations towards the end). Also, Worf has some free time, which again wouldn't work with his warrior ethos were the war ongoing - the only times he took time off were for Klingon Rituals (TM). OTOH, Worf isn't a diplomatic envoy - but quite possibly he never was, having sobered up just in time and declined the absurd proposal.
Timo Saloniemi