Revert "Remove the old HaTS implementation on API docs" (#28748)

dev/docs/survey.html

+<script async="" defer="" src="../assets/api_survey.js"></script>

dev/tools/dartdoc.dart

@@ -136,6 +136,7 @@ Future<void> main(List<String> arguments) async {
     '--inject-html',
     '--header', 'styles.html',
     '--header', 'analytics.html',
+    '--header', 'survey.html',
     '--header', 'snippets.html',
     '--header', 'opensearch.html',
     '--footer-text', 'lib/footer.html',