Project Explorer: open-closed state of folders not retained when project reopened

## Steps to Reproduce

1. Open some folders in the `lib` folder structure.
2. Restart Android Studio.
3. The folders will be displayed closed. Previously, the open-closed state of the project folders were retained when the project was reopened.

It started with AS Ladybug and the corresponding Flutter plugin update. I can't tell which one of the two is really responsible. I tried `Repair IDE`, it doesn't help.

## Version info

P:\Flutter\bin\flutter.bat doctor --verbose
[√] Flutter (Channel stable, 3.24.3, on Microsoft Windows [Version 10.0.22631.4317], locale en-US)
• Flutter version 3.24.3 on channel stable at P:\Flutter
• Upstream repository https://github.com/flutter/flutter.git
• Framework revision 2663184aa7 (5 weeks ago), 2024-09-11 16:27:48 -0500
• Engine revision 36335019a8
• Dart version 3.5.3
• DevTools version 2.37.3

[√] Windows Version (Installed version of Windows is version 10 or higher)

[√] Android toolchain - develop for Android devices (Android SDK version 34.0.0)
• Android SDK at P:/Android_SDK
• Platform android-34, build-tools 34.0.0
• ANDROID_HOME = P:/Android_SDK
• ANDROID_SDK_ROOT = p:\Android_SDK
• Java binary at: c:\Program Files\Android\Android Studio\jbr\bin\java
• Java version OpenJDK Runtime Environment (build 21.0.3+-12282718-b509.11)
• All Android licenses accepted.

[X] Chrome - develop for the web (Cannot find Chrome executable at .\Google\Chrome\Application\chrome.exe)
! Cannot find Chrome. Try setting CHROME_EXECUTABLE to a Chrome executable.

[√] Visual Studio - develop Windows apps (Visual Studio Community 2022 17.11.5)
• Visual Studio at C:\Program Files\Microsoft Visual Studio\2022\Community
• Visual Studio Community 2022 version 17.11.35327.3
• Windows 10 SDK version 10.0.22621.0

[√] Android Studio (version 2024.2)
• 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 21.0.3+-12282718-b509.11)

[√] Connected device (2 available)
• Windows (desktop) • windows • windows-x64 • Microsoft Windows [Version 10.0.22631.4317]
• Edge (web) • edge • web-javascript • Microsoft Edge 129.0.2792.89

[√] Network resources
• All expected network resources are available.

! Doctor found issues in 1 category.
Process finished with exit code 0

Reproduce with Flutter 3.24.3 and Android Studio 2024.2 using the reported steps, then trace how the Flutter plugin handles project-tree folder expansion across restart. Done means folders opened before restarting remain open when the project is reopened.

Written by the indexing model from the issue text.