You need to exit Steam completely, then restart. Now downloading for me. Otherwise it doesn't seem to trigger even when starting TSW2. It's a shame Steam/DTG can't/won't preload pre-purchased DLC as this would eliminate the delay getting started.
Make sure you really have exited - even if you close with the x in the corner you will find it still runs in the background. If in doubt switch off and restart your PC.
But now it's done. Just a little late; Steam is now telling me 2.7 GB downloaded completed at 1:11 PM.
I would think the reason they didn't pre-load this onto steam is a direct result of the actions of those who used that hacky method to download SEHS before release and then post videos about it etc. Could be wrong, but that's what I personally think.