Is gargling while rinsing the mouth during ablution from the Sunnah, and what is its proof?

Gargling is the deep movement and circulation of water within the mouth, and it is an exaggeration of rinsing the mouth. Jurists have differed regarding its ruling: The Malikis and Hanbalis, and what is apparent to the Hanafis, held the view that it is recommended to exaggerate rinsing the mouth by gargling. Whereas the Shafi’is and another opinion among the Hanafis believe that exaggerating rinsing the mouth is a Sunnah. Those who deemed gargling a Sunnah based their opinion on it being an exaggeration of rinsing the mouth, which is a Sunnah, citing the Hadith of Asim bin Laqit bin Sabrah, from his father, which states: "Perform ablution thoroughly, and exaggerate in sniffing water (into the nose) unless you are fasting." Imam An-Nawawi mentioned that exaggerating rinsing the mouth and sniffing water is a Sunnah without any difference of opinion. As for rinsing the mouth itself, it is a Sunnah of ablution according to the preponderant opinion.