Ensure plugin registrants are generated in build_web (#41906)

diff --git a/packages/flutter_tools/lib/src/web/compile.dart b/packages/flutter_tools/lib/src/web/compile.dart
index c924c3e..7644f63 100644
--- a/packages/flutter_tools/lib/src/web/compile.dart
+++ b/packages/flutter_tools/lib/src/web/compile.dart
@@ -27,9 +27,10 @@
   }
   final bool hasWebPlugins = findPlugins(flutterProject)
     .any((Plugin p) => p.platforms.containsKey(WebPlugin.kConfigKey));
+  await injectPlugins(flutterProject, checkProjects: true);
   final Status status = logger.startProgress('Compiling $target for the Web...', timeout: null);
   final Stopwatch sw = Stopwatch()..start();
-  final BuildResult result = await const BuildSystem().build(const WebReleaseBundle(), Environment(
+  final BuildResult result = await buildSystem.build(const WebReleaseBundle(), Environment(
     outputDir: fs.directory(getWebBuildDirectory()),
     projectDir: fs.currentDirectory,
     buildDir: flutterProject.directory