Move SDK logic from generic_chat example to flutter_genui package

[jacobsimionato]

This is a simple move and restructure of SDK logic out of the example app folder.

• Move everything except Firebase config and main.dart
• Put internal classes in lib/src
• Rename "widgets" folder to "core_widgets"
• Remove a little dead code and reformat some files

[gemini-code-assist]

Code Review

This pull request refactors the project by moving core SDK logic from the generic_chat example into the flutter_genui package. This includes renaming WidgetTreeLlmAdapter to ConversationManager, moving several files, and removing some dead code. The changes are well-structured and align with the PR's goal. My main feedback is to improve test coverage for the newly packaged logic, as per the repository's style guide, to ensure its stability and maintainability.

[gemini-code-assist]

According to the repository's style guide, code should be tested.¹ As ConversationManager is a core component being moved into the package, this would be a great time to add unit tests for it. Creating a conversation_manager_test.dart with tests for methods like sendUserPrompt and _handleEvents (perhaps by making it package-private for testing) using a mock LlmConnection would significantly improve the package's quality and maintainability.

Style Guide References

Footnotes

1. The style guide states that code should be tested. (link) ↩