You're right, the writers didn't write Kira like that, Nana Visitor ad-libbed all those scenes. For example, in the script for
Emissary, this is what was originally written for Kira and Sisko's first meeting.
KIRA: Yes?
SISKO: I'm Benjamin Sisko.
KIRA: I suppose you want the office.
SISKO: Well, I thought I'd say hello first and then take the office, but we could do it in any order you'd like.
KIRA: Hello.
SISKO: Is something bothering you, Major?
KIRA: No, I'm super. I just had a big bowl of ice-cream.
SISKO: What flavour?
KIRA: Raspberry ripple, it's my favourite.
SISKO: I'm more a fan of honeycomb.
KIRA: Nah, I don't like the crunchy bits. So you're from the Starfleet?
SISKO: Yes. Is that going to be a problem?
KIRA: No! I love the Federation! You guys are swell.
SISKO: I just thought you might have a problem with the Provisional Government inviting us.
KIRA: That's no problem for me, I love the Provisional Government, they're doing one heck of a job!
Frankly, I'm surprised that Nana was allowed to get away with changing the script so much because of how incapable she was of acting happy. If I had been a producer on the show, I would have fired her and hired someone that could play the role that she was supposed to, but I guess Rick Berman was a pretty terrible producer.
(I think you'll find that if you actually read the scripts of the scenes where Kira is complaining, you'll find that she's complaining in the scripts too, not just on the screen.)