[Settings WebUI] Fix Simultaneous Diplay of Password

This change fixes a UI bug where a hidden password was not correctly
updated when both the <password-list-item> and <password-edit-dialog>
were setting the same password at the same time.

Bug: 910081
Change-Id: If1ac5298ceebe1f12003083d87a85d1fa66a1f71
Reviewed-on: https://chromium-review.googlesource.com/c/1354275
Reviewed-by: Demetrios Papadopoulos <dpapad@chromium.org>
Commit-Queue: Jan Wilken Dörrie <jdoerrie@chromium.org>
Cr-Commit-Position: refs/heads/master@{#612787}