Update DeviceManagmentService metrics.

Publish the metrcis for each request type individually.

Bug: 959398
Change-Id: Ia1280fdc3c2fa328a364918c53de69e35b230003
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1594119
Reviewed-by: Jesse Doherty <jwd@chromium.org>
Reviewed-by: Owen Min <zmin@chromium.org>
Reviewed-by: Maksim Ivanov <emaxx@chromium.org>
Commit-Queue: Owen Min <zmin@chromium.org>
Cr-Commit-Position: refs/heads/master@{#662237}