Answer
I say, and with God's success: Rinsing the mouth and inhaling water through the nose are Sunnah in ablution and not obligatory; because the inside of the nose and mouth do not face each other; and as narrated from Ibn Abbas (may Allah be pleased with him): "If a man performs ghusl from janabah and does not rinse his mouth or inhale water through his nose, he should repeat the ablution, but if he leaves that in ablution, he does not have to repeat it." In the sources 1: 13, Al-Tahanawi said in I'la al-Sunan 1: 183: The hadith is good and acceptable for proof, and there is a correct witness from the narration of Ibn Sirin. And because the mouth is inward from one aspect and outward from another: in terms of sensation: when the mouth closes and opens. And in terms of ruling: in the swallowing of the fasting person’s saliva, its ruling is like that of the inward since it does not break the fast, and in the entry of something into his mouth, its ruling is like that of the outward since it breaks the fast; thus it is considered inward in ablution and outward in ghusl; because what is mentioned in ghusl is in the form of exaggeration: {And if you are in a state of janabah, then purify yourselves} Al-Ma'idah: 6. Refer to: Sharh al-Waqayah, 1: 35-36, Al-Bahr al-Ra'iq, 1/21, Durar al-Hukam, 1/11, Halabi Saghir, p.10, Al-Ikhtiyar, 1/17, and Mukhtalif al-Riwayah, p.326-327, and Allah knows best.