Second: The ḥadith of ʿĀʾishah, in which the Prophet ﷺ said, “Rinsing the mouth and drawing water into the nose are part of the wudu that one must not omit.” It was reported by Abū Bakr in al-Shāfī.
Third: What Muslim recorded (237) from Abū Hurayrah: the Prophet ﷺ said, “When any one of you performs ablution, let him inhale water into his nostrils, then expel it.”
Fourth: What Abū Dāwūd and al-Dāraquṭnī transmitted from Laqīṭ b. Ṣabrah, that the Prophet ﷺ said, “When you perform ablution, rinse your mouth.”
Fifth: The divine command to wash the face in His words, “So wash your faces” (Qurʾān 5:6), is a command to wash both organs, for the mouth and the nose are outward parts that fall under the term “face,” as mentioned earlier.
The strongest view, therefore, is the last one, because of the weight of its proofs and the absence of any evidence to the contrary.