[Code Health] Clean up stale base::Feature "GetCookiesStringUma"

This CL removes the feature flag without behavior change. A new test-
only function is added in NetworkService for tests to disable metrics
updater. The metrics updater records UMA every 30s, which makes tests
using TaskEnvironment::FastForward*() methods with long delays to time
out.

Bug: 356624966
Change-Id: I315dde5236389a929371284d1d860bf6c328d610
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6033422
Reviewed-by: Carlos Caballero Grolimund <carlscab@google.com>
Commit-Queue: Xiaochen Zhou <xiaochenzh@chromium.org>
Reviewed-by: Maks Orlovich <morlovich@chromium.org>
Reviewed-by: Andrew Paseltiner <apaseltiner@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1386245}