To what extent is the story true regarding the encounter between the Angel of Death and Noah (peace be upon him), and their conversation about worldly matters?

No authentic Marfu‘ Hadith has been reported regarding this matter. Rather, it was narrated with a weak chain of transmission on the authority of Anas, as reported by Ibn Asakir from Aban ibn Abi Ayyash, who is considered abandoned (matruk). It was also reported as Mawquf and Maqtu‘. The narration from Anas in Ibn Abi al-Dunya's chain of transmission includes Nafi‘ Abu Hurmuz, who is very weak. It was also reported as a saying of Sufyan ibn Uyaynah, Al-Hasan, and Abu Mushir, in Maqtu‘ form.