Enhance app type detection logic to include prompt analysis for Flutter references and minor relaxation in system prompts

[NamanGoyalK]

Fixes #3509

This PR addresses the issue where the AI would sometimes incorrectly default to a pure Dart context (CLI/Console) when the user intended to build a Flutter app, particularly when starting from an empty editor.

Changes

1. pkgs/dartpad_ui/lib/app/genai_editing.dart:

   • Improved the _determineAppType logic to inspect the prompt for keywords (e.g., flutter, widget, app, custompainter) if the source code is ambiguous or empty.
   • This ensures that prompts like "Create a Flutter app" correctly trigger the Flutter system prompt instead of the Dart system prompt.

2. pkgs/dart_services/lib/src/generative_ai.dart:

   • Adjusted the system prompts to allow the model to deviate from the strict "No UI" or "Flutter Only" rules if and only if the user explicitly and unambiguously requests it.
   • This provides an "escape hatch" for power users who might want to generate a Dart script while in Flutter mode (or vice versa) without the model refusing the request.

Verification

• Tested locally with prompts such as "Create a Flutter app with a CustomPainter" in an empty editor. The system correctly inferred AppType.flutter and generated the UI code.
• Verified that ambiguous prompts still default to safe baselines.

---

• I’ve reviewed the contributor guide and applied the relevant portions to this PR.

[johnpryan]

This change is unrelated to the issue as far as I can tell, could you take this out or submit this as a separate pull requests? Thanks!

[NamanGoyalK]

Thanks for the review, @johnpryan!

​I believe this logic is actually central to fixing the issue. The root cause of #3509 is that an empty editor defaults to AppType.dart, which triggers the "Pure Dart" system prompt (the one forbidding UI).

​This change allows the frontend to detect intent (e.g., "Create a Flutter app") and switch to AppType.flutter before sending the request. This ensures the backend selects the correct flutterPrompt instead of forcing the model to fight against the dartPrompt.

​Without this, we are relying 100% on the relaxed system prompt (the other change in this PR) to override the wrong context. This feels like a more robust fix, but I am happy to split it out if you strictly prefer relying on the prompt change alone.

[NamanGoyalK]

Actually @johnpryan , I see where you're coming from regarding PR scope. I've just force-pushed a version that reverts the dartpad_ui changes. Let's keep this PR focused strictly on the system prompt relaxation. I'll move the prompt-based detection logic to a separate discussion/PR. This should be ready for review now!

[github-actions]

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