Update devtools_compatibility to include new badge registration

Back-end change: https://crrev.com/c/6818486

Bug: 427371633
Change-Id: Ice2866d89fc4a7411fcc29892352335fb06fac3e
Reviewed-on: https://chromium-review.googlesource.com/c/devtools/devtools-frontend/+/6818991
Auto-Submit: Kim-Anh Tran <[email protected]>
Commit-Queue: Simon Zünd <[email protected]>
Reviewed-by: Simon Zünd <[email protected]>

Author: ktran

front_end/devtools_compatibility.js

@@ -789,6 +789,14 @@ const InspectorFrontendHostImpl = class {
     DevToolsAPI.sendMessageToEmbedder('recordPerformanceHistogram', [histogramName, duration], null);
   }
 
+  /**
+   * @override
+   * @param featureName
+   */
+  recordNewBadgeUsage(featureName) {
+    DevToolsAPI.sendMessageToEmbedder('recordNewBadgeUsage', [featureName], null);
+  }
+
   /**
    * @override
    * @param umaName