[views-ax] Migrate default kClassName

This CL migrates the kClassName to being set on the cached data
member on ViewsAccessibility. Ideally this would be done on the
ctor but since View::GetClassName is virtual then this leads to
issues.

This CL is part of the ViewsAX project:
https://docs.google.com/document/d/1Ku7HOyDsiZem1yaV6ccZ-tz3lO2XR2NEcm8HjR6d-VY/edit#heading=h.ke1u3utej413

Bug: 325137417
Change-Id: Ia16133f7038232710b1950624727821828e2f93f
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6001295
Reviewed-by: Dirk Pranke <dpranke@google.com>
Reviewed-by: Allen Bauer <kylixrd@chromium.org>
Commit-Queue: Javier Contreras <javiercon@microsoft.com>
Cr-Commit-Position: refs/heads/main@{#1395662}