I think the biological definition is “adult human organism, whose biology is built for producing large gametes”.
It might not be the best definition, but that’s what I can do without looking it up.
Where I am unsure is that I remember from school that girls are born already having all their egg-cells, but men constantly produce new sperm so even if they ruin their sperm by drinking then it takes 4 months of sobriety to have new sperm never touched by alcohol.
Then what are the people who can give birth naturally but are genetically male because they have a Y chromosome
https://novonordiskfonden.dk/en/news/more-women-than-expected-are-genetically-men/
Your definition is okay, but I would go with a human being whose twenty-third pair of chromosomes (i.e., the sex chromosomes) are XX, while a man is a human being whose sex chromosomes) are XY.
The reason that I would go down to the DNA-level like this, is that, sadly, a small number of genetic freaks out there who have, for example, XXY or XYY sex chromosomes and are hermaphrodites whose sex organs can get very weird. As such, I’m not totally comfortable with a definition of womanhood that says you’re a woman if you have this or that “part.” No, you might have that particular part and be a hermaphrodite. In reality, though, we’re talking about a very tiny segment of the human population, estimated 0.02% to 0.05%, that can’t clearly be classified as man or woman.
I would go with “Human, Adult, Female”, now if you ask what’s female that’d stump most Dems.