[ClientCerts] Update private keys convert key details to a dict

Updates the private key and its implementation to store the private
key details into a dictionary object so it can be stored later in
the browser prefs.

Bug: 392927550
Change-Id: I9305d6a06054adaf4e0665163c59b46d8d2189d5
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6264168
Commit-Queue: Hamda Mare <hmare@google.com>
Reviewed-by: Sébastien Lalancette <seblalancette@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1420461}