When it comes to J. K. Rowling and the question of whether or not she is trans, it is important to consider two aspects:
the story she is actually telling
and
the reason she is telling that story
The story comes from her TERF Wars essay that she published in June 2020. (Excellent timing to really hammer home just how much of a bigot you are.)
In that essay, she talks about her experiences with misogyny and abuse. She also talks about how she experienced OCD and about how much her father wanted her to be a boy.
An important thing to remember is that Rowling has a history of ... adjusting ... her backstory to fit whatever narrative she wants to tell. During the Heyday of Harry Potter, she (and her promotional staff) leaned heavily into her time on benefits to give her a rags-to-riches backstory. Most of that story was heavily exaggerated and some of the stuff that was said about that time had been pulled from thin air.
It's completely possible that she is doing the same thing in her TERF wars essay.
So we do not know how much of this is actually true.
There is an old interview with her and her sister, in which both of them talk about how her parents had wanted her to be a boy. They specifically talk about how her parents told her the male name they had chosen for her prior to her birth.
In that same interview, Rowling recounts an argument she had with her parents about how her gender and the gender of her sister. (Basically, Rowling brought up how their parents seemed to be fine with her younger sister being a girl and asked her parents if they were fine with her being a girl, too. They told her no.)
We also know that she has a history of being subjected to misogyny. The way some media outlets treated her in the past was pretty nasty and misogynistic. Some of it did criticize her for not being female enough.
What I can say is that she sounded genuinely bitter and distraught during that interview. She also seems to have undergone a lot of feminizing surgeries since those media outlets started to report on her. So it's completely possible that at least some of it is true.
The important thing here:
While it's completely possible that she has experienced trauma about her gender, that trauma is external. At no point did she talk about how she herself wanted to be a boy or a man because she truly felt like one. Instead, she is pretty adamant that that trauma was inflicted on her by her parents not accepting her girlhood and later by society not accepting her womanhood.
I believe I could have been persuaded to turn myself into the son my father had openly said he’d have preferred.
Which brings us to the reason for why she is telling that story. And in her essay, she is pretty clear about that, too:
Littman mentioned Tumblr, Reddit, Instagram and YouTube as contributing factors to Rapid Onset Gender Dysphoria, where she believes that in the realm of transgender identification ‘youth have created particularly insular echo chambers.’
TERF wars isn't her biography.
Or, to phrase it differently: She isn't giving you (general you) a true and heartfelt recollection of her past. She is trying to sell you a grift.
And the grift that she is trying to sell you is Lisa Littman's pseudo-scientific bullshit about Rapid Onset Gender Dysphoria.
With her essay, Rowling wants to push the narrative that trans men identifying as men is a case of social contagion. It's all about how trans boys and men aren't really trans, but confused and distressed girls who convince each other into believing that they could escape their distress by becoming men.
And that's also the reason for why she is bringing up how her daddy hated her for being a girl. She is telling that sob story, because she uses it as a way to place herself in a position of authority on the topic.
For everyone who wants to learn more about the topic, I recommend watching this video by Caelan Conrad: