[ci] Run web tests in wasm (unit + integration). (#8111)

Adds CI configuration to run web integration tests (in the master channel) compiled to Wasm.

It also removes the `build-examples` step from web integration tests, in some isolated testing:

| platform tests shard | With build-examples | Without build-examples |
|---|-----|-----|
| 1 | 30m | 21m |
| 2 | 13m | 11m |
| 3 | 17m | 10m |

## Issues

* Fixes https://github.com/flutter/flutter/issues/151664

script/tool/test/dart_test_command_test.dart

@@ -337,6 +337,33 @@ test_on: vm && browser
       );
     });
 
+    test('runs in Chrome (wasm) when requested for Flutter package', () async {
+      final RepositoryPackage package = createFakePackage(
+        'a_package',
+        packagesDir,
+        isFlutter: true,
+        extraFiles: <String>['test/empty_test.dart'],
+      );
+
+      await runCapturingPrint(
+          runner, <String>['dart-test', '--platform=chrome', '--wasm']);
+
+      expect(
+        processRunner.recordedCalls,
+        orderedEquals(<ProcessCall>[
+          ProcessCall(
+              getFlutterCommand(mockPlatform),
+              const <String>[
+                'test',
+                '--color',
+                '--platform=chrome',
+                '--wasm',
+              ],
+              package.path),
+        ]),
+      );
+    });
+
     test('runs in Chrome by default for Flutter plugins that implement web',
         () async {
       final RepositoryPackage plugin = createFakePlugin(
@@ -517,6 +544,33 @@ test_on: vm && browser
       );
     });
 
+    test('runs in Chrome (wasm) when requested for Dart package', () async {
+      final RepositoryPackage package = createFakePackage(
+        'package',
+        packagesDir,
+        extraFiles: <String>['test/empty_test.dart'],
+      );
+
+      await runCapturingPrint(
+          runner, <String>['dart-test', '--platform=chrome', '--wasm']);
+
+      expect(
+        processRunner.recordedCalls,
+        orderedEquals(<ProcessCall>[
+          ProcessCall('dart', const <String>['pub', 'get'], package.path),
+          ProcessCall(
+              'dart',
+              const <String>[
+                'run',
+                'test',
+                '--platform=chrome',
+                '--compiler=dart2wasm',
+              ],
+              package.path),
+        ]),
+      );
+    });
+
     test('skips running in browser mode if package opts out', () async {
       final RepositoryPackage package = createFakePackage(
         'a_package',