Fix flaky SW registration in PushMessaging/BudgetManager browser tests

chrome/test/data/push_messaging/service_worker.js

Index: chrome/test/data/push_messaging/service_worker.js
diff --git a/chrome/test/data/push_messaging/service_worker.js b/chrome/test/data/push_messaging/service_worker.js
index 15332d4478714b08199296d3cfb0f2686f81d92a..0e134855652b0d9035a39de5fed5584612bddb8b 100644
--- a/chrome/test/data/push_messaging/service_worker.js
+++ b/chrome/test/data/push_messaging/service_worker.js
@@ -6,6 +6,9 @@
 // which would affect the scope of the importScripts call here.
 self.importScripts('/push_messaging/push_constants.js');
 
+// Don't wait for clients of old SW to close before activating.
+self.addEventListener('install', () => skipWaiting());
+
 // The "onpush" event currently understands two values as message payload
 // data coming from the test. Any other input is passed through to the
 // document unchanged.