"'Aishah brought a patched woolen Kisa' (cloak), and a thick Izar, She said: 'The Messenger of Allah (ﷺ) died in these.'"

There are narrations on this topic from 'Ali and Ibn Mas'ud. The Hadith if 'Aishah is Hasan Sahih Hadith.
Jami` at-Tirmidhi Book 24, Hadith 14
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Some of them reported it from Hammad bin Salamah, from 'Ali bin Zaid, from Al-Hasan, from his father, from Umm Salamah.

Jami` at-Tirmidhi Book 24, Hadith 13 Next Hadith → That the Prophet (ﷺ) said: "On the day of His Lord spoke to him, Musa was wearing a wool Kisa', a wool Jubbah, a wool Kummah, wool pants, and his sandals were made of the skin of a dead donkey."

This Hadith is Gharib, we do not know of it except from the the narration of Humaid Al-A'raj. And Humaid - Ibn 'Ali Al-A'raj - I Heard Muhammad saying: "Humaid bin 'Ali Al-A'raj is Munkar in Hadith." While Humaid ibn Qais Al-A'raj Al-Makki, the companion of Mujahid is trustworthy. The Kummah is a small cap.

Jami` at-Tirmidhi Book 24, Hadith 15