That's part of the reason that "biological male" isn't a highly informative/technically-precise term, but assuming you mean something like Swyer syndrome, there isn't really a reason to worry about estrogen making them infertile, so in context using the phrase "transgender women" would have been clear regardless.
I think, since the assignment is typically done by a medical professional (at least for recording a birth certificate), the assumption is that the gender is either a quickly fixed clerical error or reflective of a phenotype that presents as sufficiently male/female to convince a professional.
"Convincing a professional" is a reasonable proxy for biological sex, given that the cases that would fool a medical professional are in many (most?) cases sufficiently ambiguous that a reasonable person could take either side for what the biological sex is.
They would continue to be male, forever. "Female" is a sex, not merely a gender identity.
At birth, nobody is "assigning" genders to you, they are attempting to observe your sex from primary sex characteristics. If they see vulva, they are observing a female; if they see penis/scrotum, they are observing a male.
While there are edge cases, it is generally pretty simple.
