Add web startup analyzer to material 3 demo (#2144)

This adds a tool to measure web app startup for the Material 3 demo.

Demo:
- [Example app](https://flutter-web-perf-experiments.web.app/)
- [Material
3](https://flutter-web-perf-experiments--material3-vswzldcy.web.app/)
(open console)

---------

Co-authored-by: Brett Morgan <brett.morgan@gmail.com>
Co-authored-by: Kevin Moore <kevmoo@google.com>

web/_packages/web_startup_analyzer/lib/src/frame_analyzer.dart

@@ -0,0 +1,43 @@
+// Copyright 2021 The Flutter team. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+import 'dart:async';
+
+import 'package:flutter/scheduler.dart';
+import 'package:flutter/widgets.dart';
+
+class FrameAnalyzer {
+  final WidgetsBinding _binding;
+  final Completer _onDone = Completer();
+  int _remainingFrames;
+
+  final int additionalFrames;
+  List<int> additionalFrameTimes = [];
+
+  FrameAnalyzer(this._binding, {this.additionalFrames = 10})
+      : _remainingFrames = additionalFrames;
+
+  Future captureAdditionalFrames() {
+    _binding.addTimingsCallback(_timingsCallback);
+    return _onDone.future;
+  }
+
+  _reportFrame(FrameTiming frameTiming) {
+    additionalFrameTimes.add(frameTiming.totalSpan.inMilliseconds);
+  }
+
+  _timingsCallback(timings) {
+    int i = 0;
+    while (_remainingFrames > 0 && i < timings.length) {
+      _reportFrame(timings[i]);
+      i++;
+      _remainingFrames--;
+    }
+    if (_remainingFrames <= 0) {
+      _binding.removeTimingsCallback(_timingsCallback);
+
+      _onDone.complete();
+    }
+  }
+}

web/_packages/web_startup_analyzer/lib/src/startup_analyzer.dart

@@ -0,0 +1,25 @@
+// Copyright 2021 The Flutter team. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+import 'dart:js_interop';
+
+@JS()
+@staticInterop
+external FlutterWebStartupAnalyzer get flutterWebStartupAnalyzer;
+
+@JS()
+@staticInterop
+class FlutterWebStartupAnalyzer {
+  external factory FlutterWebStartupAnalyzer();
+}
+
+extension FlutterWebStartupAnalyzerExtensions on FlutterWebStartupAnalyzer {
+  external JSObject get timings;
+  external void markStart(String name);
+  external void markFinished(String name);
+  external void capture(String name);
+  external void captureAll();
+  external void capturePaint();
+  external void report();
+}