I have no issue with the phrase "LEGAL sex assigned at birth", because yes legal sex is assigned (based on biology - ie biologically what you are is the default assigned to you) and can be legally changed later to match one's gender preference by going through an official process.
Trouble is, no one is "assigned" female at birth really, because it isn't really something anyone can choose (or not) and often the "assigned" is used as if biological, and not legal, sex is what is being talked about ("AFAB makes no sense, because it isn't like you can be assigned female later on). One is "born female" or "born male", with a tiny minority requiring further investigations to decide which they best fit. And then a small minority wish to express their gender differently and change their legal sex.