GF stated that VGC will keep being on SwSh for time being.Well, unless a miracle happens, seems like for a number of months Diamond and Pearl are their own thing. If we get lucky maybe everyone can play together in the future.
If Sword and Shield get updates with the new Pokemon that would be great though. Remakes would just be for the story, Sword and Shield for the online experience.
So I wouldn't expect to ever be a crossplay between SwSh and BDSP.
It's also a lot of pointless tech work simply cause while it's a (moderately) safe assumption to think that SwSh will eventually get compatibility for gen 4 pokemon when Home compatibility launches, the other way around is pretty much not happening, so it'd require a very specific game mode to let the two games fight each other (differetly from XY / ORAS who both had the same mechanics, just XY didn't have access to some of the ORAS stuff directly in the game and needed them to be imported).
Moreso when you consider that by the time Home compatibility launches, it'll also be moderately close to gen 9 announcement or even release anyway.