[Extensions UI] Update extensions page to use api methods for permissions prompt

chrome/chrome_browser_extensions.gypi

 # Copyright (c) 2013 The Chromium Authors. All rights reserved.
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
 {
   'variables': {
     'chrome_browser_extensions_chromeos_sources': [
       'browser/extensions/api/enterprise_platform_keys/enterprise_platform_keys_api.cc',
       'browser/extensions/api/enterprise_platform_keys/enterprise_platform_keys_api.h',
       'browser/extensions/api/enterprise_platform_keys_private/enterprise_platform_keys_private_api.cc',
@@ skipping 174 matching lines @@
       'browser/extensions/api/declarative_content/chrome_content_rules_registry.cc',
       'browser/extensions/api/declarative_content/chrome_content_rules_registry.h',
       'browser/extensions/api/declarative_content/content_action.cc',
       'browser/extensions/api/declarative_content/content_action.h',
       'browser/extensions/api/declarative_content/content_condition.cc',
       'browser/extensions/api/declarative_content/content_condition.h',
       'browser/extensions/api/declarative_content/content_constants.cc',
       'browser/extensions/api/declarative_content/content_constants.h',
       'browser/extensions/api/desktop_capture/desktop_capture_api.cc',
       'browser/extensions/api/desktop_capture/desktop_capture_api.h',
+      'browser/extensions/api/developer_private/show_permissions_dialog_helper.cc',
+      'browser/extensions/api/developer_private/show_permissions_dialog_helper.h',
       'browser/extensions/api/developer_private/developer_private_api.cc',
       'browser/extensions/api/developer_private/developer_private_api.h',
       'browser/extensions/api/developer_private/developer_private_mangle.cc',
       'browser/extensions/api/developer_private/developer_private_mangle.h',
       'browser/extensions/api/developer_private/entry_picker.cc',
       'browser/extensions/api/developer_private/entry_picker.h',
       'browser/extensions/api/developer_private/extension_info_generator.cc',
       'browser/extensions/api/developer_private/extension_info_generator.h',
       'browser/extensions/api/developer_private/inspectable_views_finder.cc',
       'browser/extensions/api/developer_private/inspectable_views_finder.h',
@@ skipping 848 matching lines @@
           ],
         }, {  # use_brlapi==0
           'sources': [
             'browser/extensions/api/braille_display_private/braille_controller_stub.cc',
           ],
         }],
       ],
     },
   ],
 }