Assistant is part of system UI, which is the same as shelf and launcher. I tried on launcher with the same search+a > w, it also reads "internal display". I suspect the keyboard shortcut goes up the window/view tree and reads the root window. 

The status tray window does read "Status tray", so there should be some way to make it work.  Meilin can you help take a look and fix launcher and assistant?

Just uploaded a CL and right now the screen reader will read "Assistant" when invoking that shortcut on Assistant. But I'm not sure this title is detailed enough. @aprilkuo @sgabriel Could you please take a look at this? 

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/280480c600d6ac15b68733c778917878fd0dfc3a

commit 280480c600d6ac15b68733c778917878fd0dfc3a
Author: Meilin Wang <meilinw@google.com>
Date: Mon Dec 03 22:28:37 2018

Add meaningful title of Assistant for screen reader users.

Add an accessible window title called "Assistant" for Assistant container
view, thus ChromeVox can read the window title when invoking multilayered
shortcut:Search + a > w.

Bug:  910559 
Test: local compile and manually test.
Change-Id: Ia71e08567cf448abce1e9a5d59b9fe50f34be8a2
Reviewed-on: https://chromium-review.googlesource.com/c/1357650
Commit-Queue: Meilin Wang <meilinw@chromium.org>
Reviewed-by: Xiaohui Chen <xiaohuic@chromium.org>
Cr-Commit-Position: refs/heads/master@{#613291}
[modify] https://crrev.com/280480c600d6ac15b68733c778917878fd0dfc3a/ash/ash_strings.grd
[modify] https://crrev.com/280480c600d6ac15b68733c778917878fd0dfc3a/ash/assistant/ui/assistant_container_view.cc
[modify] https://crrev.com/280480c600d6ac15b68733c778917878fd0dfc3a/ash/assistant/ui/assistant_container_view.h