[Uno-d] Plumb the signout confirmation dialog in the profile menu

Notes:
- a follow up CL will plumb the dialog in settings.
- I kept the signout logic from the profile menu, but it needs to be
  updated: we should not open the signout tab if the user is already
  signed out. tracked in b/329806665
- the dialog (https://screenshot.googleplex.com/4zTGjnstyYAirkB)
  assumes that the user is in signin paused state. However the dialog
  should be shown in all cases when there is pending data. The strings
  will need to be updated.
- currently, when in signin paused, it does not seem that butter saves
  the data in the account storage. It looks like butter is simply
  disabled and data saved in local storage. This will need to be
  updated, but until then, the dialog is hard to trigger.

Bug: b/328005358
Change-Id: Ic5744a0fd0b0aea0c7ddfb3b87a8140f20f428dc
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5372487
Reviewed-by: Alex Ilin <alexilin@chromium.org>
Reviewed-by: Victor Vianna <victorvianna@google.com>
Reviewed-by: Monica Basta <msalama@chromium.org>
Commit-Queue: David Roger <droger@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1276885}