feat: Add cached manager and optimize latex rendering with code refactoring

[GIKICoder]

🚀 Features

• Add cached manager: Implement caching functionality to improve performance
• Optimize latex rendering: Enhanced latex rendering capabilities for better user experience

🔧 Improvements

• Code organization: Restructured file organization and cleaned up codebase
• Build fixes: Resolved build-related issues
• Code cleanup: Removed unused code to reduce bundle size

📝 Examples

• Updated and added comprehensive example code
• Enhanced example documentation for better developer experience

📋 Changes Summary

• Organized file structure for better maintainability
• Fixed build bugs and compilation issues
• Removed unused/dead code
• Implemented cached manager with supporting code
• Updated example code with new features
• Optimized latex rendering performance