Describe the bug

To Reproduce

1. Open Flutter DevTools from the IDE sidebar (VS Code)
2. Select any tool (e.g., Performance, Inspector, Network, Logging)
3. DevTools panel does not respond — no action happens and the UI becomes stuck

Expected behavior

1. DevTools should open the selected tool immediately
2. The UI should remain responsive and allow switching between different DevTools tabs without freezing

Screenshots
https://github.com/user-attachments/assets/bbf2e501-7cdd-4ab6-8f69-d4a4a54079d9

Please complete the following information:

You can run the Dart: Collect Diagnostic Information command from the VS Code command palette (F1) to easily capture this information or provide it manually.

• Operating System and version: macOS Tahoe 26.1
• VS Code version: 1.106.1 (Universal)
• Dart extension version: 3.122.0
• Dart/Flutter SDK version: 3.122.0
• Target device: mobile (Android & iOS simulator)