Are you sure about that? I just found this article:
gamesradar (dot) com/diablo-2-resurrected-cross-progression-will-be-available-for-the-consoles-that-support-it-blizzard-says/
(I don’t know how to post links here …)
“Right now we are saying the consoles that support it,” Gallerani said. “That’s not us trying to be evasive, we’re just working through the exact details. What will happen is, whenever you make a character online, it’s gonna ask you to link to a BattleNet account. Obviously if you play on PC, you’re using the BattleNet launcher. But if you fire the game up on Xbox, it’s gonna say ‘Hey, does your Xbox account know about your BattleNet?’ And if it does, you can connect, because all of your online characters are stored on BattleNet servers, so it’s the exact same character that all of these games are accessing.”