To what extent are these narrations true regarding Fatimah bint Asad and her love for the Prophet, may Allah bless him and grant him peace, and her preferring him over her own children, and the reason for naming his daughter Fatimah after her?

Fatimah bint Asad al-Hashimiyyah, the mother of Ali and his brothers, embraced Islam, migrated, and passed away in Medina. She was a righteous woman, and the Messenger of Allah, peace and blessings be upon him, used to visit her and rest at midday in her home. As for the circulating reports about her in some Shiite books, especially what has been transmitted from the book "Al-Anwar" by Abu al-Hasan Ahmad ibn Abdullah al-Bakri, these are lies and fabrications, as al-Bakri is considered a liar and an imposter, and his book is full of falsehoods against Allah, His Messenger, and the Companions.