Did Sawdah (may Allah be pleased with her) depart from Muzdalifah before dawn, and if there is an excuse for departing before dawn, is there an expiation?

The Shaykh : It is narrated from Aisha (may Allah be pleased with her) that she said: "Sawdah sought permission from the Messenger of Allah (peace and blessings be upon him) to depart before him, and she was heavyset—meaning overweight—so he permitted her." Agreed upon by al-Bukhari and Muslim. Was this departure from Muzdalifah before dawn? And if there is an excuse for departing from Muzdalifah before dawn, is there an expiation? The answer: Departing before dawn is one of the rituals of Hajj. The pilgrims came from 'Arafah on the night of the festival and spent the night in Muzdalifah. Spending the night there is obligatory, and the correct view is that it is a pillar. However, women differ from men in this ruling. All women, and the children with them, are permitted to depart from Muzdalifah not only before dawn, but before dawn by a significant time, provided it is after midnight. They may depart from Muzdalifah after the middle of the night to Mina. This is a specific ruling for women and children, and some elderly men are included with them. There are explicit hadiths that the Messenger (peace be upon him) granted a dispensation for women and the weak among the children to depart and leave Muzdalifah for Mina before dawn. In that case, there is no expiation and no ransom. However, there is a point that many scholars, let alone others, overlook: women and children who take this dispensation and depart from Muzdalifah before dawn, and arrive in Mina before the sun rises, are not permitted to stone the Jamarat al-Aqabah until the sun rises. Thus, departing from Muzdalifah before dawn is a dispensation, but stoning is not permissible until after the sun rises. As for the Messenger (peace be upon him), as in the hadith of Ibn 'Abbas, Ibn 'Abbas said: "The Messenger of Allah (peace and blessings be upon him) granted a dispensation for the weak and the children to depart from Muzdalifah before dawn, and he said to them: ."