So here's a little sneak preview: Corruption is completely going away in the 9.0 prepatch, so as soon as 9.0 drops. Because canonically N'Zoth is dead, we have destroyed the Old God, his corruption has been cleansed from Azeroth. We may preserve a legacy grayed out tooltip on the gear, but it's a mix of moving the story line forward and frankly the game is pretty broken right now - we know the game is pretty broken right now - part of why that's been ok is that we know it's for a short period of time; there's no way to really deal with someone who has, you know, 100% crit rate and all of that stuff going into new content. Enjoy the silly season, but post squish we're going to get back to a normalized space and we'll retune all the content so that people can do everything that they're accustomed to doing. If you could kill N'Zoth with all your corruption before 9.0, you'll be able to do it at max level in 9.0, we don't want to change that.
Directly related, Essences and Azerite armor will continue to work. However when you go into the Shadowlands, the link between the Heart of Azeroth and the planet Azeroth is basically separate - so that will disable your Essences, it will disable the Azerite Powers on your gear while you're in the Shadowlands. If you come back to Battle for Azeroth content, they'll still function there - if you wanna go run old content for transmog or whatever, we're not completely pulling it out of the game like we did with Artifacts, but there's as story reason why it doesn't function there. You'll replace your shoulders, armor, helm pretty quickly; if you have a high level Heart of Azeroth, you'll probably still be wearing that for stats all the way to max level though.