[iOS] Avoid double taps issue in FullscreenSigninScreenCoordinator

This patch avoid to start sign-in while a sign-in is already in progress
in FullscreenSigninScreenMediator.
This fixes the issue of a double tap in
FullscreenSigninScreenCoordinator.

Fixed: 478202195
Change-Id: I10dd792ba29f850aca5e6680d8a87eb66961c8bb
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7520926
Auto-Submit: Jérôme Lebel <jlebel@chromium.org>
Commit-Queue: Arthur Milchior <arthurmilchior@chromium.org>
Reviewed-by: Arthur Milchior <arthurmilchior@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1575227}