Is snuffing water up the nose in wudu (ablution) obligatory or supererogatory, and what is the evidence for it?

Firstly: Istinshaq (drawing water into the nose) is obligatory according to the Hanbalis, and a Sunnah according to the majority of scholars, who consider the prophetic command for it to be a recommendation. They cite as evidence the Prophet’s (ﷺ) saying to the Bedouin: "Perform ablution as Allah has commanded you," and that the verse in Surah Al-Ma'idah does not mention it. The Hanbalis, on the other hand, believe that the Prophet’s (ﷺ) consistent practice of it indicates its obligation.

Secondly: As for Istinthar (expelling water from the nose), scholars have differed regarding it. Although some have reported a consensus on its recommendation, there is an existing disagreement among those who consider Istinshaq obligatory. Some scholars incline towards the view that Istinthar is obligatory because the purification of the nose is not complete without it, and because the objective is to clean the nose.