All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
The story that you mentioned is not attributed to the Prophet but it is a saying of a Companion.
Ibn Katheer mentioned it at length, longer than that which you mentioned, and then he himself ruled on it, saying, “There are other ahaadeeth that strengthen this story although many of it is derived from the Israa’eeliyyaat (stories from Jewish sources)… ”
The part of the story which you mentioned, that Allah created Aadam (Adam) from the clay of the earth that is of different color, has an authentic origin.
Abu Moosa Al-Ash‘ari, may Allah be pleased with him, narrated that the Prophet said, "Indeed Allah, The Almighty, created Aadam from a handful that He took from the whole of the earth. So the children of Aadam are in accordance with the earth: some of them are red, some are white, some are black, some are yellow, and some are a mixture (between these different colors); some are smooth; some are rough, some are bad and some are good.” [Ahmed, Abu Dawood, at-Tirmithi and Ibn Hibbaan. This is the wording of Ibn Hibbaan]
This authentic origin is mentioned by Ibn Katheer directly before mentioning that story. It seems that you did not notice that, otherwise you would not have asked this question.
However, we did not come across any narration that indicates that at first Allah sent Jibreel (Gabriel), then Meekaa'eel (Michael), and then the Angel of Death.
Allah knows best.