Revert a premature API deprecation.

The mentioned API method was deprecated this CL:
https://chromium-review.googlesource.com/c/chromium/src/+/3791772 due to
the previous prototpe is no longer in use. Also because we have a
similar set of new APIs. But the getSavedTemplates was missing an
equivalent in the new set.
This CL is to bring it back and rename it to match the rest new API set.

Previous security/privacy review is in the bug:
https://bugs.chromium.org/p/chromium/issues/detail?id=1259253

Bug: 1259253
Change-Id: I607aa8eaddef2d14c51507c181ffd3509437adea
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3885339


Reviewed-by: Toni Barzic <tbarzic@chromium.org>
Commit-Queue: April Zhou <aprilzhou@google.com>
Cr-Commit-Position: refs/heads/main@{#1062382}