How sound is the statement that all prophets performed Hajj to the House except Hud and Salih, and did the prophets Isaac, Jacob, Jesus, and Moses, peace be upon them, perform Hajj?

The pilgrimage of the prophets Isaac, Jacob, Moses, Jesus, and others to the House is mentioned in the narrations twice: in the saying: "There is no prophet but has performed Hajj to the House," and "Then no prophet remained after him but performed Hajj to it." These prophets came after Abraham, peace be upon him, and were from his descendants. Imam Ahmad also mentioned in Kitab Az-Zuhd, on the authority of Mujahid, that seventy prophets performed Hajj to the House, among them Moses, peace be upon him.