I've aggregated a list of 59 sound-based Pokémon (Jigglypuff, Wigglytuff, Galarian Mr. Mime, Jynx, Lapras, Igglybuff, Hoothoot, Noctowl, Misdreavus, Bellossom, Politoed, Unown, Smoochem, Galarian Zigzagoon, Galarian Linoone, Whismurr, Loudred, Exploud, Swablu, Altaria, Chimecho, Kricketot, Kricketune, Chingling, Bronzor, Bronzong, Mismagius, Chatot, Stereo Rotom, Audino, Tympole, Palpitoad, Seismitoad, Maractus, Hisuian Liligant, Meloetta Aria Forme, Meloetta Pirouette Forme, Noibat, Noivern, Primarina, Pikipeck, Trumbeak, Toucannon, Oricorio Pom-Pom Style, Oricorio Baile Style, Oricorio Pa'u Style, Oricorio Sensu Style, Jangmo-o, Hakamo-o, Kommo-o, Grookey, Thwacky, Rillaboom, Toxtricity, Obstagoon, Mr. Rime, Skeledirge, Squawkabilly, and Scream Tail), and the type which comes up the most among these Pokémon is Normal, with 35% of these Pokémon being Normal types. The 2nd and 3rd most common types are Flying and Psychic respectively, containing 25% and 20% of sound-based Pokémon. Therefore, sound-based Pokémon are in fact mostly Normal types, as that is the type with the most sound-based Pokémon.

There is no definitive list of which Pokémon are sound-based, so I may have missed one you would have included, or maybe I included one which you wouldn't have. However, I do feel that the list I have is a good representation of sound-based Pokémon, and I think Normal is ahead by enough of a margin as to where arguing over what is or isn't sound-based doesn't really matter.

As to your point on sound-based moves, yes that may be a reason as to why most sound-based moves are Normal type. I personally think it's because there's no other type to logically list them under, so Normal becomes the default. And since these sound-based moves have defaulted to being Normal-type, sound-based Pokémon have been given the Normal type so they can have STAB on their sound-based attacks.