Blizzard hasn't talked about what it plans to do after Shadowlands. I speculate that the longterm solution would be to do this every expansion—so in the next expansion, Blizzard might move Battle for Azeroth into the multitude of choices for new character-leveling experiences and push level-cap characters back down to 50 to start whatever expansion comes after Shadowlands—an odd hybrid of traditional MMO and a seasonal model common in plenty of modern multiplayer games.
It's hard to get a sense of an entire World of Warcraft expansion from 30 minutes of play. In my short demo, I recreated my main (a Beast Mastery Hunter) and played through the introductory quests from the Bastion zone, a heaven-like plane from Azeroth's afterlife. The minute-to-minute gameplay very much followed the formula of modern WoW questing, with a variety of tasks like challenging specific enemies to duels, helping craft things in timed minigames, and of course, killing 10 rats (well, not rats, but they might as well be).
The origins of the Shadowlands remain uncertain, but they have existed ever since mortal life first arose in the physical universe. They span all worlds, including Azeroth, on which Icecrown serves as an anchor to the Shadowlands. There are those who believe mortal souls are drawn into this dark place when they die, remaining there forever. Others hope their souls will go on to a brighter place rather than languish for eternity within the cold confines of the Shadowlands.