This phrase "sex assigned at birth" is one of the most obnoxious and unscientific terms ever invented. I think it is supposed to make one think that a fetus is just an amorphous blob of cells which immediately coalesces into a boy or a girl the moment the doctor arbitrarily declares it as such.
Gender, of course, is determined at conception. While there are some genetic disorders that prevent normal development as encoded in the chromosomes, those are very rare. And since normal development did not happen, they genuinely think and look like they are the opposite gender from what their chromosomes show.
The vast majority of those who declare themselves to be transgender are not. They either have a mental illness that causes them to believe that if they were the other gender, all of their troubles would disappear. Or they have a fetish about pretending they are the other gender. Or they are perverts who want access to female-only spaces such as locker rooms. Or they are mediocre athletes who would rather compete against women than other men. None of these have a genetic disorder that literally prevents development according to the chromosomes.
It's every bit as bad as "safe and effective mRNA vaccine" ...