Remove static accessors from SidePanelUI.

This CL is a refactor with no intended behavior change.

This CL turns SidePanelUI into an abstract base class. This CL modifies
BrowserWindowFeatures to own an instance of SidePanelCoordinator.
SidePanelUI static accessors are redirected to use
BrowserWindowFeatures.

There are slight timing differences to construction and destruction of
SidePanelCoordinator, which should have no user-visible effect. This CL
introduces the methods InitPostBrowserViewConstruction and
TearDownPreBrowserViewDestruction to BrowserWindowFeatures to handle
this more generically.

Change-Id: Ic3565fa4ff8d6b57f301f51b2bb9d9d3ed8b2f09
Bug: 346148554, 346158959, 345499793
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5612895


Reviewed-by: Caroline Rising <corising@chromium.org>
Commit-Queue: Erik Chen <erikchen@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1313689}