Initially introduced in one of Mr. Yokai's take on Pokémon GO, the Music type is Mr. Yokai's way of making a Sound type. Unlike the Sound type, which is reserved usually for Pokémon related to volume, this type is related to Pokémon based off of any types of instruments, dancing, or as its name suggests, music. This can also be for ones based off of popular musical figures. This, however, doesn't include all sound-based Pokémon such as Primarina or Jynx, for one reason or another.
Please note that these only apply to certain Pokémon games.
The Music type was mainly made as a more realistic way of implementing a Sound type, on Mr. Yokai's opinion. The main problem with a Sound type was the mechanics of the game; this would be highly problematic as Mr. Yokai puts it, since the game would have to likely go under tons of mechanic changes in sound-based moves. Though indeed it can be easily solvable if they were turned into bi-type moves, the possibility of such is highly unlikely.
Despite your (possible) beliefs, this type isn't based off of GO Fest 2021.
When it comes to typing Music Pokémon...
It is randomly primary or secondary, whatever Mr. Yokai sees as best.
Primary-types either become bi-types or have their type replaced.
Bi-types vary on Mr. Yokai's opinion. For example, Oricorio became a Music-type because it's related to dancing, and plus there exists Pokémon like Venonat that fly yet aren't Flying. The same reason applies to Mr. Rime. Primarina didn't become a Music-type because Mr. Yokai saw the Fairy part as more prominent.
Pokémon like Audino and Chatot didn't become Music-type, with the former because it is more related to hearing and the latter because despite its design being based off of a music note, it was less of a "singing" Pokémon to Mr. Yokai. If Chatot did become Music-type, then Noibat would've been also a Music-type.
Toxtricity, Galarian Mr. Mime, and Mr. Rime got Music mainly because Seadra and Psyduck aren't Water/Poison or Water/Psychic respectively despite the former having poison and the latter having psychic powers.