Add LLM application logging example for AI-powered features

[Copilot]

Adds reference implementation for integrating Logan logging into LLM-based applications, demonstrating structured logging patterns for AI features in platforms like Aweme/TikTok.

Implementation

Example/Logan-LLM-Apps/app.ts - Chat server with comprehensive logging:

• User prompt logging with session tracking
• LLM response metadata (tokens, latency, model)
• Performance metrics and error tracking
• RESTful API (POST /chat, GET /chat/:sessionId)

Example/Logan-LLM-Apps/client-example.ts - Client demonstrating API usage with axios

Example/Logan-LLM-Apps/README.md - Integration patterns and production best practices

Logging Pattern

// User interaction
LLMLogger.logUserPrompt(userId, sessionId, prompt);

// LLM response with metadata
LLMLogger.logLLMResponse(userId, sessionId, response, model, tokens, latency);

// Performance monitoring
LLMLogger.logPerformanceMetric('response_time', latency, { userId, sessionId, tokens });

All logs use structured JSON format for easy parsing. The example uses console output; README documents integration with actual Logan SDK.

Files Added

• app.ts (220 lines) - Chat application with simulated LLM service
• client-example.ts (103 lines) - Example client
• README.md - Documentation with API reference and integration guide
• package.json, tsconfig.json, .gitignore

Updated main README.md to reference new example.

Original prompt

aweme llm apps

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