This is a chain of transmission whose narrators are all trustworthy and among the narrators of both al-Bukhārī and Muslim, apart from Aḥmad ibn al-Faraj. He is weak on account of his retention, though his truthfulness is not impugned. Ibn ʿAdī said: “He is not cited as proof; he is middling.” Ibn Abī Ḥātim said: “His standing is that of truthfulness.”
I say: Someone like him may be cited as corroboration, but not adduced as proof—especially where he contradicts trustworthy narrators, as in his wording in this chain: “from his father, from his grandfather, from ʿUmar.” This is one of his errors, not an error on the part of those above him, for they are trustworthy. The correct wording is: “from his father, from ʿAmrah, from ʿĀʾishah,” as preceded in the narration of the group.
In any case, the agreement of these four in narrating this hadith from Muḥammad ibn Abī Bakr is conclusive evidence that it has an established basis from him, since it is ordinarily far-fetched that they would have colluded upon an error. When they differ concerning him, what carries weight is the version transmitted by the group, which you have already seen. They were also corroborated by ʿAbd al-ʿAzīz ibn ʿAbd Allāh ibn ʿUbayd Allāh ibn ʿUmar ibn al-Khaṭṭāb, as recorded by al-Ṭaḥāwī (3/129). This ʿAbd al-ʿAzīz is trustworthy, as are those below him in the chain; thus, it is an authentic chain of transmission.
I have also found another route from ʿĀʾishah, may Allah be pleased with her. Al-Ṭabarānī said in al-Muʿjam al-Awsaṭ (1/185/1): “Muḥammad ibn ʿAbd Allāh al-Ḥaḍramī informed us; Isḥāq ibn Zayd al-Khaṭṭābī informed us; Muḥammad ibn Sulaymān ibn Abī Dāwūd informed us; al-Muthannā Abū Ḥātim al-ʿAṭṭār informed us; ʿUbayd Allāh ibn ʿIyāz informed us, from al-Qāsim ibn Muḥammad, from her, that the Prophet, peace and blessings be upon him, said...” He then cited it without the additional wording. He said: “None narrated it from ʿUbayd Allāh except al-Muthannā, and none narrated it from him except Muḥammad and Rayḥān ibn Saʿīd.”
I say: This is a weak chain of transmission because of this al-Muthannā, who is al-Muthannā ibn Bakr al-Baṣrī. Al-ʿUqaylī said (p. 429): “No one corroborates him in his hadith.”