What does Eve’s punishment—“your desire will be for your husband, and he will rule over you” (Gen 3:16)—mean?

If not for this curse, or punishment, would Eve not desire her husband? Surely that cannot be the point. Eve’s subjection to Adam had not yet been made a matter of law. While this was implied, since Eve had been made from Adam’s rib and with Adam had named “woman,” still, it had not yet been settled clearly and definitively that Adam would be Eve’s “master” or “ruler.” That seems to be the point here. Thus Eve’s abuse of her initial prerogative serves as an origin story of the subjection of women.