Is that canon? It seems that digitalization is not a thing in Pokémon.
In Legends Arceus they explain how Pokémon can naturally become smaller and Poke Balls are just empty containers which trigger that reaction. Kinda makes sense given that Poke Balls apparently were invented before anything digital.
Idk if any game ever explains how they are then stored in the PC, but according to PokeSpe, Poke Balls are physically sent and stored in literal boxes.