Inspector: unify code to initialize and refresh replay state button and eject button.

Previously, the status would not update on load/unload, and incorrect status would
be displayed when switching to the replay dashboard midway through capturing. I
also fixed some subtle initialization order bugs.
Incorporate some coding style and conventions feedback from Timothy Hatcher.

Add missing DataProvider.Event.DataChanged event.
Remove old sync-nightly-inspector script that is no longer necessary.
Inspector: rename CaptureDid{Start,Stop} to past tense, since no CaptureWill* equivalents exist.
Inspector: start capturing asynchronously using an AsyncTask. Port AsyncTask
(previously ReplayTask) and AsyncTaskScheduler infrastructure from old UI.