I can elaborate on what I said before. The term “female,” when used about humans and without qualifiers, has always referred to both sex and gender. This is because we used to think they were one and the same.
Plus, it’s not uncommon for a trans person to change their biology through hormones and/or surgery. So they wind up having fewer “male” or “female” characteristics than they were born with. I even mentioned intersex women who have XY chromosomes, despite being assigned female at birth.
You already seem to accept that a trans man who phenotypically looks male is in fact male. Yet he still has a vagina and likely uterus, ovaries, and XX chromosomes. He’s just taken hormones and likely had top surgery to remove his breasts. The same would be true of a trans woman, except there are more surgeries possible for her: she may have a vaginoplasty to convert her penis into a vagina, and may have had a surgery to make it easier to speak in a higher range and/or to reduce an Adam’s apple. She also may have had breast implants, though the hormones themselves will add breasts.
The point is, when we use the term “female” or “male” today, we seem to always just go by how they look to us—how they present themselves. Trans men are not female, and trans women are not male.
If you need to refer to the biology, you’re just going to need to be more specific than assuming that there is one male biology and one female biology. There are traits that were classically assigned male and female, but no single “female biology” or “male biology.”
It sure seems to me that medical professionals are already working on the problem by simply by being specific. “People with vaginas” covers you even if you don’t have a uterus or are on masculinizing hormone therapy.
As for being “assigned” a gender at birth, I can explain that too. You were almost certainly assigned male at birth. The doctor or whoever was involved in the birthing process looked at you and said you were a boy, most likely simply looking at your genitals. And, from that point on. you were raised as if you were male. That’s assignment.
With a trans person, that assignment was incorrect, and they have chosen to make changes to fix that.
Aside about the assignment of intersex people:
(For intersex people, it wasn’t actually uncommon for doctors to make genital alterations to make the baby’s genitals conform to the gender binary. That’s how pervasive the male/female dichotomy myth has been in our history. Few were actually assigned intersex at birth.)