This is a good chain of transmission. Abū Yaʿlā also narrated it (4985) through another route from him.

The remainder of its routes are found with al-Ṭabarānī and Abū Yaʿlā (5052). Its basis, through the first route, is also reported through other chains from al-Aʿmash by al-Bukhārī (5000) and Muslim (7/148), with the wording:

“By Allah! I received directly from the mouth of the Messenger of Allah, peace and blessings be upon him, seventy-odd suras. By Allah, the Companions of the Prophet, peace and blessings be upon him, know that I am among the most knowledgeable of them concerning the Book of Allah, though I am not the best of them.”

The wording is al-Bukhārī’s. *

3028 — “He would pass by a cooking pot and take a bone with some meat on it, eating some of it; then he would pray without performing ablution or touching water. In another narration: He neither performed ablution nor rinsed his mouth.”

Ibn Abī Shaybah recorded it in al-Muṣannaf (1/50), and Abū Yaʿlā transmitted it from him (7/427/4449); Aḥmad also recorded it (6/161). Both said: Ḥusayn ibn ʿAlī narrated to us from Zāʾidah, from ʿAbd al-ʿAzīz ibn Rafīʿ, from ʿIkrimah and Ibn Abī Mulaykah, from ʿĀʾishah, who said: The Messenger of Allah, peace and blessings be upon him, would ... and he cited it. The wording is Aḥmad’s.

I say: This is an exceptionally authentic chain of transmission and meets the criteria of the Two Shaykhs. It is astonishing that al-Ḥākim did not include it in his Mustadrak as a report meeting the criteria of the Two Shaykhs!

As for the other narration, al-Bazzār recorded it in his Musnad (1/153/298): Aḥmad ibn Manṣūr ibn Sayyār narrated to us: Yaḥyā ibn Yaʿlā narrated to us: Zāʾidah narrated to us through the same chain.

This too is authentic. Ibn Sayyār—al-Ramadī—was unanimously deemed trustworthy, and Yaḥyā ibn Yaʿlā—al-Muḥāribī—was trustworthy and was likewise among the narrators relied upon by the Two Shaykhs.