Shiny Pokémon have been a staple in Pokémon since Pokémon Gold & Silver and returned once more in Pokémon Sword & Shield. However there are a few tweaks. First, the Shiny rate is the same as it has been at since Pokémon X & Y with it being 1 in 4096 as standard, or if you have the Shiny Charm you obtain for completing the Pokédex, the rates are 1 in 1365.33
The rates can be improved further by breeding with Pokémon from a game in another language. This changes it to 1 in 682.7 without a Shiny Charm or 1 in 512. with the Shiny Charm.
Pokémon Sword & Shield has a change where you can now encounter Pokémon at majorly higher levels than you and thus get restricted from capture until you have certain badges. For Pokémon that are restricted, they are set to prevent it from being shiny. You also cannot get given Shiny Pokémon including starters (although they can be bred), Type: Null and the Gigantamax Pikachu & Eevee gifts. You will also not see the Pokémon as shiny in the overworld until you encounter it.