I appreciate your in-depth answer.
There’s an inherent contradiction in this matter. On the one hand, it is proposed that the question is practically unanswerable or can only be answered with an inconclusive academic dissertation—in other words, the term refers to what we should regard as an arbitrary social construct with too tenuous a connection with objective reality (with biological reality, in this context), or even with no connection at all. On the other hand, trans women obviously feel the term is not meaningless and want to be recognized as women. Thus they must have something rather concrete in mind. They were not born with the typical biological traits of a human female, yet they consider that their psychology has elements or characteristics that they feel to be typical of the average adult human female. Otherwise, the feeling of being trapped in the wrong body would make no sense. This implies an obvious relation between gender and sex. But we’re told that no such relation exists! It’s all fairly incongruous.
As I see it, your inconclusive answer stems from your not wanting to be discriminatory toward trans women, and more generally toward anyone whose gender identity doesn’t match their sex. I emphatically agree with that sentiment. But why should it be assumed that a general understanding that a woman is simply an adult female is intrinsically discriminatory or transphobic? Why should pretending that there’s absolutely no difference between a trans woman and a woman be a must for supporting the rights and human dignity of the trans community?