Shouldn't the fact that the negotiator was representing the Cardassian government show that she was a participant in a democratic republic? It is kind of a given. Akaar didn't say, "The Cardassians have a democratically elected government now." The statement seemed to be about the negotiator specifically.
You're of course right that regardless of her leanings she'd be involved in the new Cardassian political system and so representing a democratic government, but we know too that some of those involved in that system don't actually want it to work, and seek a return to military rule. The Directorate went along with the democracy thing because they didn't have enough support on the ground to kick off a conflict and decided they'd be better off participating, at least in a grudging manner, and for now. They're stuck with a democracy but don't like it and many would steer it back to the "old ways" if possible. Akaar was mentioning Detrek's background, particularly her work for the Rejal administration and her support of Ghemor, to show that she was one of the Cardassian politicians who promoted the democratic platform rather than begrudgingly participating. So I assume, anyway.