[webui browser] Add intermediate SidePanelUIBase class with Show logic

SidePanelBaseUI derives from SidePanelUI and TabStripModelObserver, and
it will house the implementation code common to both
SidePanelCoordinator and another soon-to-be-added sibling class,
WebUIBrowserSidePanelUI.

This CL adds the SidePanelUIBase class itself, and moves the logic for
construction, destruction, the Show() overloads, and necessary
dependencies from SidePanelCoordinator to SidePanelUIBase.

Followups will move additional logic from SidePanelCoordinator to
SidePanelUIBase.

This is part of the WebUIBrowser project.

Bug: 439850831,439850993,393144165
Change-Id: I5ebd76b697832c90d7d28e8617d8a6b0a222a3cf
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6867295
Commit-Queue: Cammie Smith Barnes <cammie@chromium.org>
Reviewed-by: Caroline Rising <corising@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1505930}