flutter-intellij: Android SDK "Android API 29 Platform" is not found on the disk or corrupted

Steps to Reproduce

1. create a new flutter project in android studio (I selected for android, ios and web)
2. when opening main.dart observe this notification (appears by itself, when the project is just created)
3. try to configure in Project Settings -> Project and -> Modules any sdk
4. observe that android emulator vanishes from the top-right Flutter Device selection dropdown

To fix this I explicitly set up <no SDK> and the emulator appeared again in the dropdown, but the android sdk warning stays.

Version info

 % flutter doctor -v 
[✓] Flutter (Channel stable, 3.13.4, on macOS 13.4 22F66 darwin-arm64,
    locale en-AM)
    • Flutter version 3.13.4 on channel stable at
      /Users/evgeniia/development/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 367f9ea16b (7 days ago), 2023-09-12 23:27:53 -0500
    • Engine revision 9064459a8b
    • Dart version 3.1.2
    • DevTools version 2.25.0

[✓] Android toolchain - develop for Android devices (Android SDK version
    34.0.0)
    • Android SDK at /Users/evgeniia/Library/Android/sdk
    • Platform android-34, build-tools 34.0.0
    • ANDROID_HOME = /Users/evgeniia/Library/Android/sdk
    • Java binary at: /Users/evgeniia/Applications/Android
      Studio.app/Contents/jbr/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build
      17.0.6+0-17.0.6b829.9-10027231)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 14.3.1)
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • Build 14E300c
    • CocoaPods version 1.12.1

[✓] Chrome - develop for the web
    • Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2022.3)
    • Android Studio at /Users/evgeniia/Applications/Android
      Studio.app/Contents
    • 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
      17.0.6+0-17.0.6b829.9-10027231)

[✓] VS Code (version 1.81.0)
    • VS Code at /Applications/Visual Studio Code.app/Contents
    • Flutter extension can be installed from:
      🔨
      https://marketplace.visualstudio.com/items?itemName=Dart-Code.flutter

[✓] VS Code (version 1.83.0-insider)
    • VS Code at /Applications/Visual Studio Code - Insiders.app/Contents
    • Flutter extension can be installed from:
      🔨
      https://marketplace.visualstudio.com/items?itemName=Dart-Code.flutter

[✓] Connected device (3 available)
    • sdk gphone64 arm64 (mobile) • emulator-5554 • android-arm64  • Android
      14 (API 34) (emulator)
    • macOS (desktop)             • macos         • darwin-arm64   • macOS
      13.4 22F66 darwin-arm64
    • Chrome (web)                • chrome        • web-javascript • Google
      Chrome 117.0.5938.88

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

• No issues found!