Rework how notification posts are logged to statsd

Instead of writing to statsd during PostNotificationRunnable, do it after all listeners have been notified. This prepares the code to also log timing information (i.e. total time elapsed from notify() until SystemUI has been told about it).

Test: atest, manual, & statsd_testdrive
Bug: 275044361
Change-Id: I9ceb48e67c493cb434bcaac9f14734ba30271e8c