Is it permissible to pray while there is a trace of ablution water in the mouth and nose, and is that considered drinking during prayer?

There is no harm in praying with traces of water remaining in the nose or mouth. Attempting to completely rid oneself of such traces is an act of extremism and exaggeration, leading to obsessive doubts. It is sufficient to expel water from the nose after sniffing it in, and to spit out water after rinsing the mouth. The Prophet, peace and blessings be upon him, said: "Ruined are those who indulge in ‫hardship and go to extremes."