Two things here:
1) The judge was ruling on whether it was the kind of philosophical belief protected under the Equality Act of 2010. In the decision itself, the phrasing is "a philosophical belief pursuant to section 10 EqA."
That means that he was looking at whether her belief is a philosophical belief under section 10 of the Equality Act of 2010.
Here is the relevant section of Chapter 1, which described protected characteristics:
Religion or belief
(1)Religion means any religion and a reference to religion includes a reference to a lack of religion.
(2)Belief means any religious or philosophical belief and a reference to belief includes a reference to a lack of belief.
(3)In relation to the protected characteristic of religion or belief—
(a)a reference to a person who has a particular protected characteristic is a reference to a person of a particular religion or belief;
(b)a reference to persons who share a protected characteristic is a reference to persons who are of the same religion or belief.
You'll note that it says "any [...] philosophical belief".
All philosophical beliefs are protected under the Equality Act of 2010. The judge was determining whether her beliefs were a philosophical belief under the law. He goes in to detail about the criteria he uses, and why he rejected it, if you read it.
2) Rowling actually said that Forstater was "asking the judge to rule on whether a philosophical belief that sex is determined by biology is protected in law." This is essentially what Forstater was actually asking, though the belief at issue was a bit more teased out:
If here you're trying to say that Forstater was starting from the premise that her belief was philosophical and therefore protected then yes, obviously. That Rowling started from the premise that it was a philosophical belief was, at best interpretation, equivocation through lack of understanding of what the terms she was using actually meant.
I'm not about to fault Rowling for brevity, given that the Forstater case was just one of many events she felt compelled to summarize in her letter.
I'm not faulting her for brevity. I'm faulting her for being misleading.
I cannot find the part of the judgment where the Claimant says gender is not a reality, nor the part of Rowling's essay where she mischaracterizes this claim.
Of course you can't. Well, I'm still not going to repeat myself ad nauseum for you.
Again "a philosophical belief pursuant to section 10 EqA" does not encompass the whole universe of possible philosophical beliefs[...]
Legally, it does.
You are nitpicking based on a singularly uncharitable interpretation, and would do better to find a claim that is falsifiable when interpreted straightforwardly.
I'm not nitpicking. I'm explaining how Rowling was equivocating. Whether she was doing so through malice or ignorance I'm choosing not to speculate on.
As for finding a better claim, it was
you who singled that bit out, not me, because you thought it was an easy way to dismiss the entire rebuttal.