Record top-level filtering result for all invocations of filter.

Records the metric automatically for all invocation contexts of the Supervised User async (remote) filtering service. Also records a separate metric that tracks the context only.

Moves private static methods in the context of this change to internal translation unit linkage to declutter public interface.

NO_IFTTT=First CL

Bug: 384661361
Change-Id: Ifb9962cc4ba8d794805b67583fd217fd721b00f3
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6089143
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Commit-Queue: Tomek Jurkiewicz <tju@google.com>
Reviewed-by: Nohemi Fernandez <fernandex@google.com>
Reviewed-by: James Lee <ljjlee@google.com>
Cr-Commit-Position: refs/heads/main@{#1397865}