afab and amab are commonly used abbreviations in the trans community. They stand for Assigned Female at Birth and Assigned Male at Birth.

Cis men don't describe themselves as "amab" they just describe themselves as men.

Absolutely "assigned” is used to describe a potentially imperfect decision by the nurse to label a baby male or female, based on the limited information they have at the time.

There's a lot more to gender than just what the nurse sees when you pop out, even for cis people, but what gets written down doesn't take anything else into account.

Trans people have typically thought this stuff through a lot and are using words carefully, whereas you seem resistant both to the meaning of the verb "assigned" and the context "at birth".