Declutter: Add tab-organization-selector-button

Creates a new TabOrganizationSelectorButtonElement class and references
it from TabOrganizationSelectorElement. This button contains all current
styling. Uses placeholders for text and icons, will plumb these through
in a follow-up.

Screenshot: https://screenshot.googleplex.com/55CAhg74DEnFein
Bug: 358383322
Change-Id: I43aef48cbb91da30f2a0ddde10ad501a0d0d790b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5819577
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Reviewed-by: Shibalik Mohapatra <shibalik@chromium.org>
Commit-Queue: Emily Shack <emshack@chromium.org>
Reviewed-by: Kyle Horimoto <khorimoto@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1348361}