My feeling is that after the Dominion came into the picture, they couldn't explore the Gamma Quadrant much, so there was little use for her in that capacity.
Indeed. Like when Kira says they gave up the Bajoran caste system and everyone became a soldier during the occupation.
I think that as DS9 was more of an ensemble some of the science stuff was divided between Jadzia, O'Brien, Nog, Rom and Bashir (to a lesser extent).
She still did the science stuff when needed but her position as the 3rd (and 4th officer after Worf) gave her a different focus during the war.