[toolbarpinning] Fix passwords bubble reopening on icon press

Bug: 358459176
Change-Id: I76a501988adba2147490005600cbf8679d33e0a0
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5791066


Reviewed-by: Avi Drissman <avi@chromium.org>
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Commit-Queue: Joseph Park <josephjoopark@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1345052}