Bump deps and min SDKs, move web apps to new bootstrapping logic (#2292)

Also removed the web measurement experiment from the material 3 demo

web/_packages/web_startup_analyzer/example/lib/main.dart

@@ -2,6 +2,8 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
+// ignore_for_file: avoid_print
+
 import 'dart:convert';
 
 import 'package:flutter/material.dart';

web/_packages/web_startup_analyzer/example/pubspec.yaml

@@ -3,7 +3,7 @@ description: "flutter_web_startup_analyzer example"
 publish_to: 'none' # Remove this line if you wish to publish to pub.dev
 version: 1.0.0+1
 environment:
-  sdk: ^3.3.1
+  sdk: ^3.4.0-0
   flutter: ^3.16.0
 dependencies:
   flutter:
@@ -14,6 +14,6 @@ dependencies:
 dev_dependencies:
   flutter_test:
     sdk: flutter
-  flutter_lints: ^3.0.0
+  flutter_lints: ^4.0.0
 flutter:
   uses-material-design: true