After Legion the Silithus events play out the same way. The Horde finds azerite first and the Alliance attacks the goblin miners there.
The Alliance begins to think that Sylvanas is primarily behind whatever the Horde has planned with Azerite and while the Night Elf forces move to Silithus to cut off the mining operations, Stormwind prepares to move on Undercity. The Siege of Lordaeron happens as in game. But the Alliance move not just to destroy Undercity, but reclaim all of Lordaeron and eradicate the Forsaken.
The surviving Forsaken flee to Orgrimmar where the leaders of the Horde decide that the Alliance is planning an attack from Northern Kalimdor with the purpose of finally dismantling the Horde. They decide to mobilize the Kalimdor Horde forces and launch a sneak attack (as happened in game) into Ashenvale before the Night Elf military in Silithus returns.
The Horde pushes their way to Teldrassil where Sylvanas makes the decision to burn the tree to completely shatter any Alliance holdings in Kalimdor. While Saurfang and Baine do not love this idea they see the necessity of driving the Nelves out completely and go along with it. Thus there is no civil war 2.0 and while the burning of Teldrassil is still a horrendous action it can be supported as necessary and not just an unnecessarily evil action.
Both factions then decide they need a navy to prevent any further attacks from the other continent, so they turn to Zandalar and Kul’Tiras. The leveling zones play out the same way.
This would have in my opinion fight much better with not only the characterizations of both factions and many characters, it would have given both faction fan bases justification for what their side is doing. The Alliance would be attempting to reclaim Lordaeron, prevent Sylvanas from obtaining Azerite. While the Horde would be actually attempting to protect themselves from an overzealous Alliance.