[Bookmarks Bar] Only show scrollbars when needed in popup

This CL updates the pop up menu for the bookmarks bar to look at the
measured height to determine whether or not scrollbars should be
shown.

Bug: 446206488
Change-Id: I71024c841af7e639a8e5040d69c9f33470f1b363
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6974092
Auto-Submit: Mark Schillaci <mschillaci@google.com>
Reviewed-by: Eleanor Lee <eleanorlee@google.com>
Commit-Queue: Mark Schillaci <mschillaci@google.com>
Cr-Commit-Position: refs/heads/main@{#1519474}