Kissing the back of the hand, regardless of in the Material Realm or the Magic Kingdom, has always been an ancient form of etiquette.
This manner of greeting, known in the Material Realm as the "hand-kissing ritual," is often reserved for very formal occasions, where it is used either to express respect for a distinguished lady or demonstrate loyalty from a subordinate to a superior. However, as times have changed and society in the Material Realm has moved towards modernization, such customs have gradually faded from everyday life.
Nowadays, the hand-kissing ritual is mostly found in various films, literary works, and the like, becoming a rather romantic gesture. Therefore, among the younger generation, it's perceived as a gesture of intimacy and romance. So when this form of greeting was displayed, regardless of what Asou Haruka herself thought, the young Magical Girls from Fangting City and Bai'an City were all abuzz, spontaneously letting out exclamations of various pitches.