[flutter_tools] update web template to remove some absolute paths (#52040)

diff --git a/packages/flutter_tools/templates/app/web/index.html.tmpl b/packages/flutter_tools/templates/app/web/index.html.tmpl
index d7de3a4..2fc5899 100644
--- a/packages/flutter_tools/templates/app/web/index.html.tmpl
+++ b/packages/flutter_tools/templates/app/web/index.html.tmpl
@@ -9,13 +9,13 @@
   <meta name="apple-mobile-web-app-capable" content="yes">
   <meta name="apple-mobile-web-app-status-bar-style" content="black">
   <meta name="apple-mobile-web-app-title" content="{{projectName}}">
-  <link rel="apple-touch-icon" href="/icons/Icon-192.png">
+  <link rel="apple-touch-icon" href="icons/Icon-192.png">
 
   <!-- Favicon -->
-  <link rel="shortcut icon" type="image/png" href="/favicon.png"/>
+  <link rel="shortcut icon" type="image/png" href="favicon.png"/>
 
   <title>{{projectName}}</title>
-  <link rel="manifest" href="/manifest.json">
+  <link rel="manifest" href="manifest.json">
 </head>
 <body>
   <!-- This script installs service_worker.js to provide PWA functionality to
@@ -24,7 +24,7 @@
   <script>
     if ('serviceWorker' in navigator) {
       window.addEventListener('load', function () {
-        navigator.serviceWorker.register('/flutter_service_worker.js');
+        navigator.serviceWorker.register('flutter_service_worker.js');
       });
     }
   </script>