If you want to grab a Shiny Meloetta for yourself, you’re going to have to first own Pokémon Scarlet and Violet, and both parts of The Hidden Treasure of Area Zero DLC.
For the first time in Pokémon history, Shiny Meloetta is available for all players to claim for free. There is one big hurdle you will have to clear before doing so in Pokémon HOME, however.