feat: refactor system prompt with Claude Code best practices

- Add new Tone and Style section emphasizing conciseness with examples
- Add Proactiveness section for balanced action-taking
- Add Following Conventions section for code style guidance
- Add enhanced Task Management section with detailed todo list examples
- Reorganize prompt sections for better flow
- Remove redundant rules that are now in dedicated sections
- Update tests to reflect new prompt structure

Author: roomote