What is the authenticity of the story of Abd al-Muttalib’s vow to sacrifice one of his sons in exchange for ten sons, and his ransoming of him with one hundred camels, which Islam affirmed as the blood money for killing? Has any of the early or later scholars commented on it? What is the opinion on it if no one has commented on it?

The story referenced in the question, concerning "the son of the two sacrificed ones," is mentioned in books of سير (biographies), تاريخ (history), and حديث (Prophetic traditions) with similar wordings. However, no authentic chain of transmission (sanad) has been found for it, and no scholar has ever ruled it to be authentic. Al-Hakim narrated it in Al-Mustadrak with a weak chain of transmission, which Al-Dhahabi described as "flimsy" (wahin). The narrations mention that Mu'awiyah narrated from the Prophet, peace and blessings be upon him, the story of the Bedouin who called him "O son of the two sacrificed ones," and that the two sacrificed ones are Isma'il and Abdullah ibn Abd al-Muttalib, whom his grandfather Abd al-Muttalib vowed to sacrifice and ransomed with one hundred camels. Given the weakness of its chain of transmission, and because it does not pertain to a legal ruling, an action, or a belief, it is not appropriate to waste time scrutinizing its authenticity.