Pixel 6 Pro emulator visible in Device Manager but not detected by Flutter device selector

## What happened

I created a new Pixel 6 Pro Android Emulator in Android Studio Device Manager.

The Pixel 6 Pro AVD is visible in Device Manager and launches successfully. However, after launching it, the Pixel 6 Pro does not appear in the Flutter device selector / Running Devices list.

Only my existing Pixel 6A emulator is shown.

The Flutter application builds successfully, but I cannot select the Pixel 6 Pro as a Flutter target device.

## Steps to reproduce

1. Open Android Studio.
2. Open Device Manager.
3. Create a Pixel 6 Pro Android Virtual Device.
4. Launch the Pixel 6 Pro emulator.
5. Wait until the emulator finishes booting.
6. Open the Flutter device selector / Running Devices.
7. Pixel 6 Pro is not listed.
8. Pixel 6A is still listed.

## Expected result

The running Pixel 6 Pro emulator should appear in the Flutter device selector and should be available as a Flutter run target.

## Actual result

Pixel 6 Pro is visible in Device Manager and launches successfully, but it is not shown as an available Flutter device.

## Environment

Android Studio: Meerkat Feature Drop | 2024.3.2 Patch 1

Flutter plugin: io.flutter 87.0

Dart plugin: 243.27824.5

Flutter: 3.24.0

Dart: 3.5.0

## Exception

I also receive this exception from the Flutter IntelliJ plugin:

java.lang.ClassCastException:
io.flutter.toolwindow.ToolWindowBadgeUpdater$BadgeIcon cannot be cast to com.intellij.openapi.util.ScalableIcon

The exception occurs inside the Flutter IntelliJ plugin's ToolWindowBadgeUpdater.

## Additional information

The application builds successfully:

✓ Built build/app/outputs/flutter-apk/app-debug.apk

However, the newly launched Pixel 6 Pro emulator is not available as a Flutter target device.

Start by reproducing the issue with the Pixel 6 Pro AVD and inspect the Flutter IntelliJ plugin's ToolWindowBadgeUpdater, where the reported ClassCastException occurs. Then trace how running emulators are surfaced in the Flutter device selector. Done means the Pixel 6 Pro appears as a Flutter run target without the reported exception.

Written by the indexing model from the issue text.