[views-ax] Deprecate 2 functions in ash::TrayBackgroundView

This is the final CL of a multi-CL progression towards deprecating
TrayBackgroundView::GetAccessibleNodeData and
TrayBackgroundView::GetAccessibleNameForTray. Deprecating these
functions is the final step in migrating how TrayBackgroundView and its
derived classes set their accessible names. These classes now update
their accessible names in the ViewsAX cache at time of construction and
any times their accessible name changes ("push") instead of calculating
the value of their names only when requested ("pull").

Now that derived classes of TrayBackgroundView no longer depend on
these two functions, this CL removes the functions completely.

As part of the ViewsAX project, we are removing GetAccessibleNodeData
from Views across chromium:
https://docs.google.com/document/d/1Ku7HOyDsiZem1yaV6ccZ-tz3lO2XR2NEcm8HjR6d-VY/edit

Bug: 325137417, 379818907
Change-Id: I842e8a810fd41ae9b339d4bd0f48c649291ba2e5
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6120970
Reviewed-by: Benjamin Beaudry <benjamin.beaudry@microsoft.com>
Reviewed-by: Ahmed Mehfooz <amehfooz@chromium.org>
Commit-Queue: Evelynn Kaplan <evelynn.kaplan@microsoft.com>
Cr-Commit-Position: refs/heads/main@{#1401997}