Square shinies do not carry over into Scarlet and Violet. If a square shiny Pokemon is transferred into one of these games, it will appear with the standard shiny animation instead.
If you transfer it back into Sword and Shield, it's highly unlikely that the game will just delete the data that makes it a square shiny. It'll go back to a square shiny when it's in a game that has them.
Shiny Pokemon (Bulbapedia)