[TabDeclutter] Implement FindStaleTabs mojo method.

This does not handle excluded tabs. That functionality will be done in a later CL.

This CL also adds a TabDeclutterController to the TabSearchUI webui controller so that the page handler can query for the right tab declutter controller instead of using GetLastActive.
This value is set by the TabSearchBubbleHost before the bubble is shown.

Low-Coverage-Reason: HARD_TO_TEST
Bug: 365567864
Change-Id: I63558d15c1e13d9b1ac9a935980a9c0643cd894b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5845596
Reviewed-by: Erik Chen <erikchen@chromium.org>
Commit-Queue: Shibalik Mohapatra <shibalik@chromium.org>
Reviewed-by: Thomas Lukaszewicz <tluk@chromium.org>
Reviewed-by: Keren Zhu <kerenzhu@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1356334}