What is the story of Idris, peace be upon him, longing for the Garden of Eternity, and why did Al-Majnun particularly single him out for this longing, unlike other prophets?

He might be referring to the story of Idris’s yearning for Paradise—the lengthy account mentioned by some exegetes and chroniclers, which is likely from the Israʼiliyyat (Judeo-Christian traditions). Its summary is that the Angel of Death was a friend of Idris and accompanied him on his devotional journey. Idris then asked him to show him Paradise. So, the Angel of Death took him to the gate of Paradise, and when the gate was opened, Idris was so overcome by its coolness and pleasantness that it captivated his heart. He requested to enter it, ate from its fruits, and drank from its water. After entering, Idris refused to leave, clinging to the trunk of a tree within it.