There’s possibly some confusion here 
So Diablo 2 Resurrected is using an updated game engine whether you’re in the newer graphics mode or switch to see the ‘legacy’ look. This game doesn’t work the same as Starcraft II Remastered, the 2000 version of Diablo II still exists as it’s own standalone entity with it’s own servers etc.
As for the issues with D2R, we are tracking some problems with the game not launching at all for some players as per this thread.
Hope that helps!