The Quran tells us what to do and how to do. .
For example, the Quran tells us to do ablution before the Salat. It also tells us how to do ablution.
The Prophet strictly followed the Quran.
Rinsing mouth and nostrils are not part of ablution and cannot be part of the Prophet's sunnah.
The Prophet's sunnat as the messenger of God was not different from God's Sunnat.
[69:44] Had he uttered any other teachings.
[69:45] We would have punished him.
[69:46] We would have stopped the revelations to him.
The Prophet followed the Quran. So, we should do the same.
Thank you and may God guide us,