Implement OpenAI Integration in LLMService

[FJiangArthur]

Priority: High
Phase: 3
Estimate: 4 story points

Description:
Implement OpenAI API integration in LLMServiceImpl to enable AI-powered conversation analysis.

Current Issues:

• LLMServiceImpl exists but lacks actual AI integration
• No API communication with OpenAI
• Analysis methods return placeholder data

Acceptance Criteria:

• OpenAI API client is properly configured
• API authentication works with API keys
• Conversation text can be sent for analysis
• Analysis results are returned in proper format
• Error handling for API failures is implemented

Implementation Location:
lib/services/implementations/llm_service_impl.dart