[cast] Break up metrics client

Refactor out the browser part of CastMetricsServiceClient into a
separate class. This enables CastMetricsServiceClient to be used by
clients that don't include the browser.

This CL also moves CastMetricsServiceClient into chromecast/metrics.

Bug: b/129712290
Test: CQ
Merge-With: eureka-internal/269937
Merge-With: eureka-internal/263637
Change-Id: Ic75d733e826ede60339cc74bf3260622f2583d5e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1588524
Reviewed-by: John Abd-El-Malek <jam@chromium.org>
Reviewed-by: Luke Halliwell <halliwell@chromium.org>
Reviewed-by: Sean Topping <seantopping@chromium.org>
Commit-Queue: Ralph Nathan <ralphnathan@google.com>
Cr-Commit-Position: refs/heads/master@{#661548}
16 files changed