Moves the settings changed logging for statsd.

Previously, we wrote a log entry regardless of permission checks, so
the logging could be misleading. Now we only send the log to statsd
after verifying that this setting mutation is valid.

Test: Flashed onto marlin-eng and verified stats-log as expected.
Bug: 73493944
Change-Id: I2a8b052aa8c380ffc5d15caec089fffcdc5823f4