This phrase really gets on my tits. It is terribly strange use of language.
"Assigned at birth".
I've given birth three times. No-one "assigned" my children as anything at birth. My various midwives had a quick look and told me a fact: girl or boy. (I am leaving intersex out of this, since I have no experience of it.)
"Assigned at birth" conjures up people employed to go around labour wards with clipboards, saying, "Yes, well, we've had ten births today. We've assigned six of them to be male already. This one just has to be female, in order to fulfil my quotas, there we go."
It is just a weird use of language, to say that babies are "assigned" their sex at birth, rather than just observed to have female genitals or male genitals.