[Passwords] Extract method to compute the password shown in bubbles

This is a mechanical change the extracts a method used to compute the
password in the manage password bubble.

This is to avoid duplicating the funcationality for the new version
of the bubble.

Bug: 1382017
Change-Id: If3e398384e325a5b1bc0bc0fed471ad72d03a54e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4026046


Commit-Queue: Mohamed Amir Yosef <mamir@chromium.org>
Reviewed-by: Vasilii Sukhanov <vasilii@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1071558}