The battle cries of the tribes on the day of Badr

It is narrated from Sayyidah Aishah (may Allah be pleased with her) that on the day of Badr, the Messenger of Allah (peace and blessings be upon him) appointed as the battle cry (shi'ar) of the Muhajirun "Ya Abd al-Rahman", of the tribe of Aws "Ya Bani Abdillah", and of the tribe of Khazraj "Ya Bani Ubaydillah".
This is a gharib (singular) hadith with a sahih (authentic) chain, but the two Shaykhs (Bukhari and Muslim) did not record it; regarding battle cries, they recorded the narration of al-Zuhri from Sayyiduna Kathir bin Abbas from his father about the day of Hunayn, in which the battle cries of the tribes are mentioned.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that four hundred households, or four hundred men, of the tribe of Azd Shanu'ah came to the Prophet (peace and blessings be upon him) as a delegation, and he (peace and blessings be upon him) said: "Welcome to the people of Azd, the most beautiful of people in face, the purest in the fragrance of their mouths, the bravest in encounter and the most trustworthy in keeping a trust. Your battle cry (shi'ar) shall be 'Ya Mabrur'."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.