Repository: flutter
Issue: [`DropdownMenu`]  menu appears behind the keyboard
Labels: platform-android,framework,f: material design,has reproducible steps,P2,found in release: 3.7,found in release: 3.9,team-android,triaged-android

## Steps to Reproduce

<!-- Please include full steps to reproduce so that we can reproduce the problem. -->
1. Tap on textfield part
2. Menu appears
3. After tiny delay keyboard appears over the top of the menu
4. Tap the textfield twice to hide and show the menu and it appears in the correct place


**Expected results:** 
Menu show where it is not hidden

| | |
| --------------- | --------------- |
<img width="400" src="https://user-images.githubusercontent.com/12197609/227489960-2ace1a16-044e-4004-9f71-28ded03d0ab1.png"> | <img width="400" src="https://user-images.githubusercontent.com/12197609/227489976-49cb9898-ec47-4bb6-a9d1-60101031e4f6.png">


**Actual results:**
Menu hidden

<details>
<summary>Code sample</summary>


```
import 'package:flutter/material.dart';

class TestWidget extends StatelessWidget {
  const TestWidget({super.key});

  @override
  Widget build(BuildContext context) {
    final List<DropdownMenuEntry> years = List.generate(20, (i) {
      final val = (DateTime.now().year - i).toString();
      return DropdownMenuEntry(value: val, label: val);
    });
    return Column(
      mainAxisAlignment: MainAxisAlignment.center,
      children: [
        DropdownMenu(
          hintText: 'Placeholder',
          dropdownMenuEntries: years,
          menuHeight: 300,
        ),
      ],
    );
  }
}

```

</details>

<details>
  <summary>Logs</summary>


<!-- Finally, paste the output of running `flutter doctor -v` here. -->

```
[√] Flutter (Channel stable, 3.7.6, on Microsoft Windows [Version 10.0.22621.1413], locale en-GB)
    • Flutter version 3.7.6 on channel stable at C:\sdks\flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 12cb4eb7a0 (3 weeks ago), 2023-03-01 10:29:26 -0800
    • Engine revision ada363ee93
    • Dart version 2.19.3
    • DevTools version 2.20.1

[√] Windows Version (Installed version of Windows is version 10 or higher)

[√] Android toolchain - develop for Android devices (Android SDK version 33.0.0)
    • Android SDK at C:\Users\pchar\AppData\Local\Android\Sdk
    • Platform android-33, build-tools 33.0.0
    • Java binary at: C:\Program Files\Android\Android Studio\jre\bin\java
    • Java version OpenJDK Runtime Environment (build 11.0.12+7-b1504.28-7817840)
    • All Android licenses accepted.

[√] Chrome - develop for the web
    • Chrome at C:\Program Files\Google\Chrome\Application\chrome.exe

[√] Visual Studio - develop for Windows (Visual Studio Professional 2022 17.5.3)
    • Visual Studio at C:\Program Files\Microsoft Visual Studio\2022\Professional
    • Visual Studio Professional 2022 version 17.5.33516.290
    • Windows 10 SDK version 10.0.19041.0

[√] Android Studio (version 2021.2)
    • Android Studio at C:\Program Files\Android\Android Studio
    • Flutter plugin can be installed from:
       https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
       https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build 11.0.12+7-b1504.28-7817840)

[√] VS Code (version 1.76.2)
    • VS Code at C:\Users\pchar\AppData\Local\Programs\Microsoft VS Code
    • Flutter extension version 3.60.0

[√] Connected device (4 available)
    • sdk gphone64 x86 64 (mobile) • emulator-5554 • android-x64    • Android 13 (API 33) (emulator)
    • Windows (desktop)            • windows       • windows-x64    • Microsoft Windows [Version 10.0.22621.1413]
    • Chrome (web)                 • chrome        • web-javascript • Google Chrome 111.0.5563.110
    • Edge (web)                   • edge          • web-javascript • Microsoft Edge 111.0.1661.51

[√] HTTP Host Availability
    • All required HTTP hosts are available

• No issues found!
```

</details>