[A11y] Implement a lifecycle for the AXObjectCacheImpl

Design doc:
https://docs.google.com/document/d/1aJ7MtXFFRRrF_6gB12Kx1f4ZgvkOOyrLG-42--N0jY0/edit

In the document, there was a discussion regarding separation of the
concept of the lifecycle stage from what's allowed, when. This CL uses
the approach of adding StateAllowsFoo() methods to implement this
separation.

Renamed UpdatingTree, etc. to FinalizingTree to help with comprehension.

Bug: none
Change-Id: I358d9b3839cdfaf659d37e8d9ffaa3ae10d3ff1a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5604789


Reviewed-by: Chris Harrelson <chrishtr@chromium.org>
Commit-Queue: Aaron Leventhal <aleventhal@chromium.org>
Reviewed-by: Mark Schillaci <mschillaci@google.com>
Cr-Commit-Position: refs/heads/main@{#1312959}