[Extensions] Omit the "Inspect popup" menu item for synthesized actions

chrome/browser/extensions/extension_context_menu_model.cc

Index: chrome/browser/extensions/extension_context_menu_model.cc
diff --git a/chrome/browser/extensions/extension_context_menu_model.cc b/chrome/browser/extensions/extension_context_menu_model.cc
index 849956d55a34cd5cefcf1750030bfff08c7bb321..b5079f99b7a8ff81cfd0168db00b65baf9609a6d 100644
--- a/chrome/browser/extensions/extension_context_menu_model.cc
+++ b/chrome/browser/extensions/extension_context_menu_model.cc
@@ -348,8 +348,11 @@ void ExtensionContextMenuModel::InitMenu(const Extension* extension,
     AddItemWithStringId(MANAGE, IDS_MANAGE_EXTENSION);
   }
 
+  const ActionInfo* action_info = ActionInfo::GetPageActionInfo(extension);
+  if (!action_info)
+    action_info = ActionInfo::GetBrowserActionInfo(extension);
   if (profile_->GetPrefs()->GetBoolean(prefs::kExtensionsUIDeveloperMode) &&
-      delegate_ && !is_component_) {
+      delegate_ && !is_component_ && action_info && !action_info->synthesized) {
     AddSeparator(ui::NORMAL_SEPARATOR);
     AddItemWithStringId(INSPECT_POPUP, IDS_EXTENSION_ACTION_INSPECT_POPUP);
   }