[flutter_tools] resolve requests to web directory in debug mode (#51995)

diff --git a/dev/bots/test.dart b/dev/bots/test.dart
index 59b4029..8d37433 100644
--- a/dev/bots/test.dart
+++ b/dev/bots/test.dart
@@ -588,6 +588,7 @@
   await _runWebStackTraceTest('profile');
   await _runWebStackTraceTest('release');
   await _runWebDebugTest('lib/stack_trace.dart');
+  await _runWebDebugTest('lib/web_directory_loading.dart');
   await _runWebDebugTest('test/test.dart');
 }