[ Tool ] Set `VM_SERVICE_URL` to the VM service URL for web driver tests

Fixes https://github.com/flutter/flutter/issues/172220

packages/flutter_tools/lib/src/drive/web_driver_service.dart

diff --git a/packages/flutter_tools/lib/src/drive/web_driver_service.dart b/packages/flutter_tools/lib/src/drive/web_driver_service.dart
index 75e7e08..5b89e8e 100644
--- a/packages/flutter_tools/lib/src/drive/web_driver_service.dart
+++ b/packages/flutter_tools/lib/src/drive/web_driver_service.dart
@@ -51,6 +51,7 @@
 
   late ResidentRunner _residentRunner;
   Uri? _webUri;
+  final _connectionInfoCompleter = Completer<DebugConnectionInfo>.sync();
 
   @visibleForTesting
   Uri? get webUri => _webUri;
@@ -109,6 +110,7 @@
     final appStartedCompleter = Completer<void>.sync();
     final Future<int?> runFuture = _residentRunner.run(
       appStartedCompleter: appStartedCompleter,
+      connectionInfoCompleter: _connectionInfoCompleter,
       route: route,
     );
 
@@ -221,11 +223,13 @@
       await window.setLocation(const math.Point<int>(0, 0));
       await window.setSize(math.Rectangle<int>(0, 0, width, height));
     }
+    final DebugConnectionInfo debugConnectionInfo = await _connectionInfoCompleter.future;
     final int result = await _processUtils.stream(
       <String>[_dartSdkPath, ...arguments, testFile],
       environment: <String, String>{
         ..._platform.environment,
-        'VM_SERVICE_URL': _webUri.toString(),
+        if (debugConnectionInfo.wsUri != null)
+          'VM_SERVICE_URL': debugConnectionInfo.wsUri.toString(),
         ..._additionalDriverEnvironment(webDriver, browserName, androidEmulator),
       },
     );