Pokémon Scarlet and Violet's file size seems to be 10 GB
That's approximately 4 GB more than Legends: Arceus
A bunch of news about the next Pokémon titles was dropped this morning, but it looks like a little more has leaked out. According to the eShop listing for the titles, if you download them it’ll take up 10 GB of space on your Switch.
For comparison, Sword and Shield took up around 12.4 GB each, while Legends: Arceus took up 6.1 GB. The exact number could change before launch or with patches, but it seems safe to say that Scarlet and Violet will be pretty big.