While the expansion kicks off with heavy references and scenes of this war, leveling through the Horde side of the new content it barely came up again. Except for all the times I had to mine Azerite to make sure my faction was the leader in the Azeroth version of a nuclear arms race. The Alliance side of things had some heavier references to to the war, at least in the portions I played, with one scenario in Stormsong Valley where a fleet of Horde aggressors bombed a town.
Something to keep in mind as well is that this will make enchanting materials more valuable, since it is likely most players will now simply scrap their boe greens instead of getting them disenchanted. Also redundant dungeon/raid gear can be scrapped rather than traded to the (guild) enchanter in the run. Less stuff gets disenchanted, meaning there will be less ecnhanting materials, meaning their value will rise. All the more reason to DE rather than scrap as an ecnhanter.