Remove useDefineForClassFields=false in c/b/r/password_manager.

As part of this update, declared various missing Polymer properties,
where they were previously only declared as class members (in some cases
discovered via newly failing tests after removing
useDefineForClassfields=false).

Bug: 389737066
Change-Id: Ice4b87a43ca57618248c5698860aa1bf6364ce3a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6418635
Commit-Queue: Viktor Semeniuk <vsemeniuk@google.com>
Auto-Submit: Demetrios Papadopoulos <dpapad@chromium.org>
Reviewed-by: Viktor Semeniuk <vsemeniuk@google.com>
Cr-Commit-Position: refs/heads/main@{#1441382}