They are still their biological sex because that's the result of genes and chromosomes, not macroanatomy and hormones. All the surgical procedures themself call it cosmetic surgery because that's what a vaginoplasty is. You're not 'cutting off' the penis, you're reforming it into a vulva. All men can grow breasts, and when you give males estrogen that breast develop will greatly increase.
Not to offend, I think many of the prettiest women in the world were born males, but it's basicly no different than if I wore a dress and wig and a padded bra. Am I now a woman because I look (kinda, blur your eyes hehe) like a woman, or am I still a man?
While there are in fact at least 6 biological sexes in humans (male, female, intersex, hermaphrodites, and 2 'hybrids' of the other 4,) there are perhaps unlimited genders. While we used to assume chromosomes were the end of the discussion and we're either XX (female,) or XY (male) we know now that that's not all there is, nor is everyone with a Y chromosome then male as you may be born with a penis, scortum, etc. while having just XX chromosomes.
Those who sometimes report feelings like women trapped in a man's body are at least in some instances literally that. Unfortunately, until we can change chromosomes and genes, we're in fact 'stuck; however we're born. Can change how we look and comform to some legal definition of biological sex, but not literally change that. Not yet. Near-future? I think we'll be able to as we're already maing same-sex reproduction possible and not throughthe previous surrogacy method but using both same-sex partner's own cells.