What is the wisdom behind mentioning the verses that show the occurrence of error or sin on the part of the Prophet, peace and blessings be upon him, and to what extent did that occur from him?

The supplication of the Prophet (peace be upon him), "O Allah, cleanse me from my sins," is an act of humility, an expression of servitude, and a teaching for the Ummah, not an indication of actual sins on his part, for he is infallible and forgiven for all his past and future sins.

Quranic verses such as: "May Allah pardon you! Why did you grant them permission?" (Quran 9:43), "Indeed, Allah has turned in forgiveness to the Prophet" (Quran 9:117), and "O Prophet, fear Allah" (Quran 33:1) do not indicate that he (peace be upon him) committed sins. Rather, they have other interpretations that are consistent with his infallibility. The reproach in the first verse was a form of honor. "Turned in forgiveness" means Allah forgave him or raised him from one state to a higher one. And "fear Allah" means to remain steadfast in piety.

Prophets are infallible in conveying the message and are protected from major and minor sins (according to the majority opinion). They may err in worldly and jurisprudential matters not related to revelation and the message. This is how the Companions interacted with him (peace be upon him) in consultation.