Does the Hadith of Zayd ibn Arqam indicate that the wives of the Prophet are not included among his Ahl al-Bayt, based on his statement: "His Ahl al-Bayt are his origin and his close relatives upon whom sadaqah was forbidden after him"?

Zayd ibn Arqam clarified that the المقصود (intended meaning) of "Ahl al-Bayt" (People of the Household) in the Hadith (definition) of the Two Weighty Things, those upon whom charity is forbidden, are the relatives of the Prophet, peace and blessings be upon him, and not his wives. For a man may divorce his wife, and she returns to her family. However, another narration of the hadith clarifies that the Prophet's wives, peace and blessings be upon him, are part of his household, but they are not included among those upon whom charity is forbidden. Whereas the families of Ali, Aqil, Ja'far, and Abbas are those upon whom charity is forbidden. Furthermore, the context of the Quran indicates that the Prophet's wives, peace and blessings be upon him, are included in His saying, the Almighty: (Indeed, Allah only intends to remove from you the impurity, O people of the household, and to purify you with [complete] purification). Therefore, Zayd ibn Arqam's statement that charity is not forbidden for the Prophet's wives is a personal ijtihad (definition) (independent reasoning), and the issue of forbidding charity for the Mothers of the Believers is a matter of scholarly disagreement.