[Vertical Tabs] Remove production usages of BrowserView::tabstrip

Removes the last production usage of BrowserView::tabstrip renaming it
to BrowserView::tab_strip_for_testing.

A separate effort will handle the consolidation of TabScrubber into
HorizontalTabStrip.

Change-Id: I54308c271c83df6a4965332779c32106bc6ce90b
Bug: 465190040, 465835455
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7404205
Reviewed-by: Georg Neis <neis@chromium.org>
Commit-Queue: Darryl James <dljames@chromium.org>
Reviewed-by: Steven Luong <stluong@chromium.org>
Reviewed-by: Eshwar Stalin <estalin@chromium.org>
Reviewed-by: Elly FJ <ellyjones@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1565998}