The problem with that being that the rest
of the technology in the world isn't quite up to that spec. Digitalizing matter has a lot of required supporting technologies, or other implications. For starters, the fact that item/Pokémon cloning, rather than being glitches, would be trivial. Or the possibility that a sadistic hacker could delete
I think we can assume the bag works similar to a Pokéball, or else the bag is a bag but you keep groups of items in Pokéballs in the bag.
Internet storage, I can't see working without raising aforementioned problems. A simple teleportation network as we see in the anime and manga could work, though I have to wonder why people
can't then teleport between Pokécenter computers.
The warp tiles I have an explanation for- they're basically a double-ended Pokéball. Send something in one side, immediately take it out the other. Probably experimental in Red/Blue days, but we see them coming into more common use now, albeit in high-budget facilities.