[web] Use benchmark callback from `dart:ui_web` (#132087)

Depends on https://github.com/flutter/engine/pull/44461
Fixes https://github.com/flutter/flutter/issues/130175
Part of https://github.com/flutter/flutter/issues/126831

dev/benchmarks/macrobenchmarks/lib/src/web/recorder.dart

@@ -10,6 +10,7 @@ import 'dart:js_interop';
 import 'dart:js_interop_unsafe';
 import 'dart:math' as math;
 import 'dart:ui';
+import 'dart:ui_web' as ui_web;
 
 import 'package:flutter/foundation.dart';
 import 'package:flutter/gestures.dart';
@@ -1335,8 +1336,7 @@ void registerEngineBenchmarkValueListener(String name, EngineBenchmarkValueListe
 
   if (_engineBenchmarkListeners.isEmpty) {
     // The first listener is being registered. Register the global listener.
-    web.window['_flutter_internal_on_benchmark'.toJS] =
-        _dispatchEngineBenchmarkValue.toJS;
+    ui_web.benchmarkValueCallback = _dispatchEngineBenchmarkValue;
   }
   _engineBenchmarkListeners[name] = listener;
 }
@@ -1347,7 +1347,7 @@ void stopListeningToEngineBenchmarkValues(String name) {
   if (_engineBenchmarkListeners.isEmpty) {
 
     // The last listener unregistered. Remove the global listener.
-    web.window['_flutter_internal_on_benchmark'.toJS] = null;
+    ui_web.benchmarkValueCallback = null;
   }
 }