There is some ambiguity but not path dependent since other path has no love option. As I understood from both MC's and Kaija explanation that they get in a relationship before Kaija saw MC that way but within time, that idea grow on her. Ambiguity came from 2 different sources as I see it besides they did not say directly. First one, they don't have Day 0 neither of them asked each other and second one, MC has those feelings long before they became a couple, maybe as early as their childhood. So, it is hard to put in a time frame. Why I think it's this way? First of all, when Kaija said at the beginning nothing was real beside the friendship I think this is a serious reference because the beginning part cannot refer the duty because they were friends before she got the orders, so this beginning she is talking about must be their relationship. Thus, I think, she is saying at the beginning of our relationship except our friendship everything was a lie. Therefore, they became a couple then Kaija's love started.
Here I disagree with your interpretation. I can't check the exact quotes right now, but by "at the beginning" I'd understand that to mean at the beginning of her assignment, not a relationship. Even if they were already friends, she still probably started to spend even more time with MC as a result of this orders, even if just as a friend.
If she started a relationship with only friendship and without attraction or affection, it'd directly contradict other statements she made that she didn't enter into one to make her job easier or under false pretenses.
I'd also wager that 99% of people start relationships with people before it becomes full blown love, so as long as the initial interest was legitimate, I don't know that I'd consider it fake if they started a relationship or became lovers before it had progressed to love. Again, it's a gradual transition from initial attraction to love that often developed alongside the relationship itself.
As jobs part of their life, that is correct but this is not a job she can quit, she can move away, she can stay away of MC. She has to interact with MC because of her orders, she is stuck with him. So, not organic.
Others have left the Templars, so I somewhat disagree that she has no choice. Granted, her other job prospects are likely very limited given her specialized skills etc.
And if she truly has no choice but to spend time with MC, then she lacks agency in that matter and can't be held responsible for doing so. Therefore, from the perspective of just her and MC, I'd still consider it organic, even if in the broader sense it's less so.