Move extension API schema registration to ExtensionsClient.

extensions/DEPS

 include_rules = [
   "+components/url_matcher",
   "+content/public/common",
   "+crypto",
   "+grit/extensions_resources.h",
   "+testing",
   "+ui",
 
   # Temporarily allowed includes as part of the app shell/extensions refactor.
   #
   # NOTE: Please do not add includes without talking to the app shell team;
   # see OWNERS for this directory.
   #
   # TODO(jamescook): Remove these. http://crbug.com/162530
   "!chrome/browser/chrome_notification_types.h",
-  '!grit/extensions_api_resources.h',
   # This is needed for renderer JS sources which should eventually move to
   # the extensions_resources target.
   "!grit/renderer_resources.h",
 ]
 
 specific_include_rules = {
   ".*(test|test_util)\.(cc|h)$": [
     "+content/public/test",
 
     # Temporarily allowed testing includes.  See above.
@@ skipping 16 matching lines @@
   ],
   "(simple|complex)_feature_unittest\.cc|base_feature_provider_unittest\.cc": [
     "+chrome/common/extensions/features/chrome_channel_feature_filter.h",
   ],
   "permissions_data_unittest\.cc": [
     "+chrome/common/chrome_version_info.h",
     "+chrome/common/extensions/extension_test_util.h",
     "+chrome/common/extensions/features/feature_channel.h",
   ],
 }