So that what made her so strict? I was anticipating something much worse not that I want t...

It couldn't have been two chapters actually, as this was the principal obstacle to Kaoruko's and Rintaro's relationship.
Also, the incident might have seemed anticlimactic because you're reading it in a story. Try to have empathy and put yourself in the teacher's shoes.
She was a young teacher in her first years of teaching (young teachers are usually much more involved emotionally with their students), her student feel off a cliff. A cliff. She was extremely lucky to come out with only a broken arm (if my memory is correct). But it's not the incident which made the teacher hate Chidori, it's the reaction of the boyfriend as well as his friends'.
They laughed about it and overall mocked the girl (+kikuo). In the teacher's mind, her student almost died (she already felt guilty for not stopping her from going) and the boy responsible for it mocked her precious student

Honestly from a teacher's perspective and also the fact that its a prestigious school I'm sure it must be hell
(Though I was indeed also expecting smt like SA)

I don't think the boyfriend was friends with the guys who caused her to fall off the cliff, seeing as they were still on good terms during that hospital visit. But it was definitely the nonchalant and downright disrespectful attitude that the boys responsible had about the whole situation that really fueled her disdain for chidori

the boyfriend didn't mock the girlfriend, it was the other guys who were involved in the incident (who caused the boyfriend to bump into her girlfriend accidentally) were blase about the situation from what I gather from the story but now I have to recheck to make sure

The problem is not with the matter of what happened in itself, it's the building up of the story and the way it was written and translated. And it could very well be because of editing restrictions and exigence where the author had to make concessions. But I stand by the fact that after all that, the way it resolves and the original issue and trauma is anticlimactic. As a story.

The trauma in itself is not the problem or "not enough"

I agree with this, the story even after rereading it did set up the problem of the 2 school's division to be much worse than what we actually got. I don't find fault with the actual incident but it does indeed feel like there was more planned