Fix flaky SW registration in PushMessaging/BudgetManager browser tests

chrome/test/data/push_messaging/push_test.js

Index: chrome/test/data/push_messaging/push_test.js
diff --git a/chrome/test/data/push_messaging/push_test.js b/chrome/test/data/push_messaging/push_test.js
index 24ef5ea221f73b05c5a12ed6cf5a64e67323696d..180f1a622860570361433804d1dc4c6b9e53575f 100644
--- a/chrome/test/data/push_messaging/push_test.js
+++ b/chrome/test/data/push_messaging/push_test.js
@@ -44,10 +44,11 @@ function registerServiceWorker() {
   // The base dir used to resolve service_worker.js and the scope depends on
   // whether this script is included from an html file in ./, subscope1/, or
   // subscope2/.
-  navigator.serviceWorker.register('service_worker.js', {scope: './'}).then(
-      function(swRegistration) {
-        sendResultToTest('ok - service worker registered');
-      }, sendErrorToTest);
+  navigator.serviceWorker.register('service_worker.js', {
+    scope: './'
+  }).then(swRegistrationReady).then(() => {
+    sendResultToTest('ok - service worker registered');
+  }).catch(sendErrorToTest);
 }
 
 function unregisterServiceWorker() {