Nobody is claiming that trans people are biologically identical to their gender. That's a stupid straw man, and a moment's thought would reveal it - in the context of this particular discussion alone. If people were insisting that trans people were biologically identical to their gender, then how could the argument be made that trans men can menstuate?
But even leaving aside the whole trans vs TERF issue, Rowling's statement was stupid and wrong anyway. The article in question was about menstruation. Therefore "people who menstruate" is a better term than "women". Do you kow why? Again, just take a moment to think about it. You yourself referred to schools. Why schools? Because school pupils menstruate. An ex-girlfriend of mine started menstruating when she was 9. Did that make her a woman? Are you making the argument that the schoolgirls you referred to are women?
So, even if we were to accept the argument that trans people are only their biological sex, it's still not only women who menstruate.
There's a problem in Rowling's statement from the other direction as well. The implication that "people who menstruate" is synonymous with "women" is implies that people who don't menstruate are not women. So anybody who's gone through the menopause is no longer a woman. A relative of mine had a hysterectomy in her 20s. Did she cease being a woman then?
If you address an article to "women", and then exclude a large number of women, then you'd be better off using a term that better describes who the article is aimed at/talking about. Like "people who menstruate". Because that's what the article was about - menstruation, rather than gender or biological sex.
Rowling was being stupid and, judging by her history of being a TERF, she was also being bigoted.
Don't fall into the trap of reflexively agreeing with something stupid that someone has said just because it aligns with your prejudices. Apply some thought first. In this case it really shouldn't take much to see the obvious flaws in Rowling's tweet.