[Android][Passwords] Add public implementation and use of backend

This CL introduces a public implementation for the backend factory
which allows to use it at all.
The implementation needs to be overridden by a downstream
implementation as provided in https://crrev.com/i/4086348. Therefore,
only land this afterwards or official builders will break again.

Bug: 1229654, 1245727
Change-Id: Ib8d877a9e9b6c50b12590a7f053581dcf1ad79db
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3139999


Commit-Queue: Friedrich [CET] <fhorschig@chromium.org>
Reviewed-by: Boris Sazonov <bsazonov@chromium.org>
Cr-Commit-Position: refs/heads/main@{#918724}