Yes, there is a simple definition (adult human female), but the judge gave a better answer, noting what the judge has to know, and noting that there are bioligical issues that one should ask a biologist about.

She would have been in trouble if she had answered with the simple definition, because legally a person can identify as a woman in the US, though she(he) has male and female reproductive organs. In the US, there is no legal 3rd gender recognition, whereas India recognises a 3rd gender, or hermaphroditism as a legal gender. This may indeed be a topic for the Supreme Court in the near future, thanks to popular right-wing concerns about transgender people. The judge is likely well aware of this, given the politicization of gender in the US. My view is that this is a private matter, not political.

The judge is not required to know specific gender definitions. And as we know, a true definition of 'woman' is a bit more than this, as regards gender, sexuality, and biology. Yes, there is the simple definition, but it can be unfairly applied to hermaphrodites and transgender people who identify as women in the US. Perhaps a resolution to this can be a legal recognition of the 3rd gender and transgender (if not a hermaphrodite in the latter case).

There are anomalies in human biology whereby a woman might have a penis. It's a myth that this cannot happen. Read here: https://www.newsweek.com/can-woman-have-penis-gender-identity-myths-explained-1093051

Regarding your other points, I am not suggesting that anyone change the definiton of 'woman' or that the definition is relative to parrticular social circumstances.

Regarding your points about rape in prison, laws against rape and assault are the same regardless of gender.