I want to react to some of the things you addressed. But if I have misunderstood you, please say so.
Yes, that’s why we have separate male and female competitions in sports. It is not as if female athletes train less than male athletes. Leonard Sax wrote a book on how male and female brains differ, and how parents and teachers can use this info (“Why Gender Matters”).
Nonetheless, these differences are not essential to establish a proper definition of male and female. See below.
We only know about chromosomes for a very short time. Our ancestors didn’t need those to decide whether someone is male or female. Like Trent Horn, I prefer a teleological definition. Women are naturally ordered towards gestation. (That doesn’t mean they are always capable of it, which may be caused by any reason.) Men are naturally ordered towards impregnation (idem). That’s why we use the terms father and mother.
Regarding intersex, I want to mention three things. This also relates to @St.Roymond 's very personal story. So I realise this is a sensitive issue for many people. I hope my remarks exhibit a graceful tone.
First
“For one, “intersex” does not mean “neither male nor female.” There are more than 16 different conditions classified as intersex, or more accurately “disorders of sex development” or “differences of sex development” (DSD’s). These disorders/differences refer to atypical features in one’s sex-chromosomes, reproductive organs, or anatomical sex (or two of the three, or all three). …
Almost everyone with these conditions typically experience no ambiguity in their biological sex.”
Sex, Gender, and Transgender Experiences: Part 6—What about Intersex? | The Center for Faith, Sexuality & Gender
Second
There is a clear difference between intersex and transgender. The biological sex of intersex people can not always be established (with our current knowledge). But transgender ideology says that the social construction of sex (which they sometimes call gender) can be different from your (established) biological sex.
Third
“The Bible’s big story is uniquely able to explain why the reality we experience now is sometimes different from how God originally intended things to be. We know that our corporate rebellion against God has led to brokenness and imperfections in God’s originally perfect creation (Genesis 3; Romans 8:20-22), and we know that this brokenness extends also to our physical bodies (Romans 8:23). It should therefore not be a surprise to us when our physical bodies, whether from birth or later in life, exhibit divergences from God’s original plan for human embodiment. All of us experience this to a greater or lesser extent at various points in our lives. …
“With this understanding, we can see how the existence of intersex conditions doesn’t disprove the reality of the gender binary. The gender binary is there as a part of God’s good creation, but it, like all creation, can be marred by the effects of sin.”
https://thinktheology.co.uk/blog/article/the_binary_and_intersex
Male and female societal roles change through time. Yet e.g. a tomboy is still naturally ordered towards gestation. What society expects from men and women can change. But God’s teleological vision for men and women will always remain the same.