Not every woman is going to kiss you on the first date. I would almost wonder, with her wanting to pay her own way if she is actually trying to signal that she isn't into you like that. There are women who think that by paying (or offering to pay) they are sending the
message that they are not interested.
Other times women may be more cautious romantically, not yet comfortable enough, etc. Some are downright shy. I did not kiss my ex-husband on the first several dates even though I found him very sexy. I wanted to be certain he liked me and was not toying with me since he had many women to choose from, and I also wanted the tension and desire to build (both for myself and for him.)
In her particular case I think she is fence sitting really but is trying to feel like in her mind she didn't breach whatever situation she is in with the other guy she is seeing. She may like you but she is already seeing someone and perhaps feels bad about allowing herself to kiss someone else. She thinks she has disclosed it to you and set boundaries, but you aren't staying in bounds, which she isn't sure what to do about. She's uncomfortable. That's how I read it as a woman.
Uncomfortable is not necessarily a bad thing. You are on her mind, hence all the texts she has sent you. Your silence is building tension (to a point).
Nexting over this is for amateur night. You are an experienced dude. Watch the rest of her actions. If you like her see her again. Go for a walk or do something else that is altogether free. You do not want to come off as over-eager either, as it can be a turn off, but each interaction between two people is different and one must learn to read the demeanor of the other party.
Sometimes I think people here get too caught up in what they are doing and they forget to pay attention to the cues the woman is giving. Continuing to try and kiss may work or it may completely backfire with someone who you otherwise might have had a shot with.
I've personally experienced both the confidently persistent approach (the article on the other part of the site is very good IMO) and eventually kissed the guy but I've had many more instances when it was a total turn off and gave me the impression that the guy was a selfish a$$. I've also had first dates where I was delighted to be kissed. There is not a one size fits all solution to this situation. You need to read the interaction as it occurs and take whatever action is most in line with the rapport you have built to that point.