[null-safety] update tests and tool auto-detection for null safe dart (#69405)

Disable null safety auto-detection for the web
diff --git a/dev/bots/test.dart b/dev/bots/test.dart
index 1e240c3..e41a6e1 100644
--- a/dev/bots/test.dart
+++ b/dev/bots/test.dart
@@ -912,6 +912,7 @@
       '--driver=test_driver/transitions_perf_e2e_test.dart',
       '--target=test_driver/transitions_perf_e2e.dart',
       '--browser-name=chrome',
+      '--no-sound-null-safety',
       '-d',
       'web-server',
       '--$buildMode',