Enable the Fetch API for extensions which service workers are supported.

extensions/renderer/dispatcher.cc

Index: extensions/renderer/dispatcher.cc
diff --git a/extensions/renderer/dispatcher.cc b/extensions/renderer/dispatcher.cc
index 34324e2be1bf10a27c375337e720fd03c5a85029..f65cf4df96955bd039811c1abff7a239e538ba40 100644
--- a/extensions/renderer/dispatcher.cc
+++ b/extensions/renderer/dispatcher.cc
@@ -1567,12 +1567,15 @@ void Dispatcher::RequireGuestViewModules(ScriptContext* context) {
 }
 
 void Dispatcher::AddChannelSpecificFeatures() {
-  // chrome-extension: resources should be allowed to register a Service Worker.
   if (FeatureProvider::GetBehaviorFeature(BehaviorFeature::kServiceWorker)
           ->IsAvailableToEnvironment()
-          .is_available())
-    WebSecurityPolicy::registerURLSchemeAsAllowingServiceWorkers(
-        WebString::fromUTF8(kExtensionScheme));
+          .is_available()) {
+    // If chrome-extension: is allowed to register service workers, register it
+    // as an allowed scheme for both service workers and the Fetch API.
+    WebString scheme = WebString::fromUTF8(kExtensionScheme);
+    WebSecurityPolicy::registerURLSchemeAsAllowingServiceWorkers(scheme);
+    WebSecurityPolicy::registerURLSchemeAsSupportingFetchAPI(scheme);
+  }
 }
 
 }  // namespace extensions