Fix structure of pkg:integration_test (#137283)

The private _ libraries should not be advertised as importable. Moving them to the src directory.

I noticed this while browsing our dart docs. This should remove the underscore entries.

![image](https://github.com/flutter/flutter/assets/1227763/41511efe-4eb8-487a-9758-ccde1720e05a)

Replaces https://github.com/flutter/flutter/pull/137197.

packages/integration_test/lib/common.dart

@@ -285,9 +285,6 @@ class WebDriverCommand {
 ///
 /// Depending on the platform the communication between `integration_tests` and
 /// the `driver_tests` can be different.
-///
-/// For the web implementation [WebCallbackManager].
-/// For the io implementation [IOCallbackManager].
 abstract class CallbackManager {
   /// The callback function to response the driver side input.
   Future<Map<String, dynamic>> callback(

packages/integration_test/lib/integration_test.dart

@@ -14,10 +14,10 @@ import 'package:flutter/widgets.dart';
 import 'package:flutter_test/flutter_test.dart';
 import 'package:vm_service/vm_service.dart' as vm;
 
-import '_callback_io.dart' if (dart.library.html) '_callback_web.dart' as driver_actions;
-import '_extension_io.dart' if (dart.library.html) '_extension_web.dart';
 import 'common.dart';
+import 'src/callback.dart' as driver_actions;
 import 'src/channel.dart';
+import 'src/extension.dart';
 
 const String _success = 'success';
 

packages/integration_test/lib/_callback_io.dart → packages/integration_test/lib/src/_callback_io.dart

@@ -8,8 +8,8 @@ import 'dart:ui';
 import 'package:flutter/services.dart';
 import 'package:flutter_test/flutter_test.dart';
 
-import 'common.dart';
-import 'src/channel.dart';
+import '../common.dart';
+import 'channel.dart';
 
 /// The dart:io implementation of [CallbackManager].
 ///
@@ -19,12 +19,12 @@ import 'src/channel.dart';
 CallbackManager get callbackManager => _singletonCallbackManager;
 
 /// IOCallbackManager singleton.
-final IOCallbackManager _singletonCallbackManager = IOCallbackManager();
+final _IOCallbackManager _singletonCallbackManager = _IOCallbackManager();
 
 /// Manages communication between `integration_tests` and the `driver_tests`.
 ///
 /// This is the dart:io implementation.
-class IOCallbackManager implements CallbackManager {
+class _IOCallbackManager implements CallbackManager {
   @override
   Future<Map<String, dynamic>> callback(
       Map<String, String> params, IntegrationTestResults testRunner) async {

packages/integration_test/lib/_callback_web.dart → packages/integration_test/lib/src/_callback_web.dart

@@ -4,7 +4,7 @@
 
 import 'dart:async';
 
-import 'common.dart';
+import '../common.dart';
 
 /// The dart:html implementation of [CallbackManager].
 ///
@@ -14,8 +14,8 @@ import 'common.dart';
 CallbackManager get callbackManager => _singletonWebDriverCommandManager;
 
 /// WebDriverCommandManager singleton.
-final WebCallbackManager _singletonWebDriverCommandManager =
-    WebCallbackManager();
+final _WebCallbackManager _singletonWebDriverCommandManager =
+    _WebCallbackManager();
 
 /// Manages communication between `integration_tests` and the `driver_tests`.
 ///
@@ -26,7 +26,7 @@ final WebCallbackManager _singletonWebDriverCommandManager =
 /// WebDriver APIs.
 ///
 /// See: https://www.w3.org/TR/webdriver/
-class WebCallbackManager implements CallbackManager {
+class _WebCallbackManager implements CallbackManager {
   /// App side tests will put the command requests from WebDriver to this pipe.
   Completer<WebDriverCommand> _webDriverCommandPipe =
       Completer<WebDriverCommand>();

packages/integration_test/lib/src/callback.dart

+// Copyright 2014 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+export '_callback_io.dart' if (dart.library.html) '_callback_web.dart';

packages/integration_test/lib/src/extension.dart

+// Copyright 2014 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+export '_extension_io.dart' if (dart.library.html) '_extension_web.dart';