...So keeping her conscious and focused and thus capable of administering the medication would be a worthwhile goal, best accomplished through the chit-chat. Apart from its morale-raising value, of course. The movie has no stardate and no specific references to the overall timeline, so most probably it takes place some time after the war. That would be the proper time for forging alliances and fortifying one's positions both politically (Picard) and physically (Worf's assignment, barely heard in the background dialogue). That would also be the proper time to do business with people who were on the opposite side in the actual conflict. (Sure, at the end of DS9 and also the war, Worf is recovering from a hangover only to learn he has been made Ambassador. But his being back in uniform and not in diplomatic attire is in no contradiction of this: Worf might not have lasted long in that position, assuming he ever actually received it.) Timo Saloniemi
While that's technically correct, there's also no reason to think it doesn't take place approximately when it was aired (during the events of 'It's Only a Paper Moon' in DS9's 7th season)- they talk about suffering losses from the Dominion, about how their diplomatic corps is busy with Dominion negotiations, about how they badly need allies, about how the So'na produce ketracel white (which, you're right, would indicate that it was after the war, but alliances may have shifted mid-war as a result of the briar patch discovery)- certainly nothing to invalidate your theory, except that Worf is not the Klingon ambassador in 'Insurrection' (so far as we can tell), he's just on assignment.
My episode order list (based on the original air dates for each episode) has Insurrection taking place shortly after AR-558 and before the Breen enter the conflict.
They did a great job in getting me to like Lisa, even though we never got the chance to see her alive. Finding out that she was beyond rescuing when they seemed so close, it was just sad.