I partially agree with this. Women are women and men are men but only in terms of biology, which is their bodies and reproductive functions. Everything else is shared, or in other words, is not gendered.
You mention that individual brains are wired differently and this is true, but this, again, is not gendered into "male wiring" and "female wiring". Surely you've seen in families where the daughter's personality is more like her father's, and the son's personality is more like his mother's, yet neither the son nor daughter experiences any gender issues? Both men and women have the ability to experience the full breadth of human emotion and they have equal abilities to develop similar interests. Generations ago in our society, interests were more gendered than they are today. There was a wider chasm between what men and women did during the 1950s than today. But this is no longer true. And interests are influenced by social constructs, they are not innate. If a girl grows up being told that girls don't tinker with cars, she won't. But if she grows up in a world that tells her she is perfectly capable to fix her own car, she will.
Last year my car battery died. I wanted to save money so I called a good female friend who also likes to save money, (she isn't paid as much as the men in her department), and she came over to help me remove it, drove us to the automotive store to buy a new one, and drove us back so we could install it. Does this mean we have male brain wiring? I don't think so.
Nikki, women don't experience what you describe. We're not struggling with identify issues, so when we look at ourselves in the mirror, we don't experience what you do. What you experienced was deep happiness over having achieved a physical transformation that erased your male gender cues, which I think is rather common among this forum's membership if they achieve the same thing. But, respecfully, feeling happiness because we look like women is not something that we experience. We rather know we are women, because we are, and this doesn't bring us to the depths of happiness as it did with you. We feel rather neutral about it, the same way a man feels about being male. Does this make sense?