Clean up SyncInternalsMessageHandler observing

This is a follow-up to r253009.  That CL was committed without
addressing all reviewer comments in order to meet a deadline.

This version cleans up that code with the help of a ScopedObserver.

BUG=346244

Review URL: https://codereview.chromium.org/178673004

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@253420 0039d316-1c4b-4281-b951-d872f2087c98
SVN changes up to revision 253420