What is the authenticity of the narration that the Prophet (peace be upon him) took off his sandals during prayer and that people took off their sandals because of his action?

The hadith in question is authentic and well-established. It was narrated by Ahmad, Al-Hakim, Abu Dawud, and others, on the authority of Abu Sa’id Al-Khudri, that the Prophet, peace and blessings be upon him, took off his sandals during prayer. So, the Companions took off their sandals. When he asked them about the reason for this, they informed him that Gabriel had told him there was impurity on his sandals. Then he said: “When one of you comes to the mosque, let him look: if he sees any impurity or dirt on his sandals, let him wipe it off, and pray in them.” This hadith was authenticated by Al-Hakim, Al-Dhahabi, Al-Albani, and Shu'ayb Al-Arna'ut.