What does it mean for a story to be from the Israʼiliyyat? Can a Prophetic Hadith be from the Israʼiliyyat? And do we accept it?

"Isra'iliyat" is a term that encompasses what Muslims adopted from the narratives of Jews and Christians, whether orally or in writing, for lessons and admonition, based on the Prophet's (peace be upon him) saying: "Narrate from Banu Isra'il (the Children of Israel), and there is no harm [in doing so]," provided that its falsehood is not known and it does not contradict the Qur'an and Sunnah. The Prophet's hadiths are not part of the Isra'iliyat, and whatever among them consists of reports about Banu Isra'il is true and firmly established because it is revelation.