feat: add OpenAI integration with dependency injection support

- Add OpenAIAdapter class using official OpenAI SDK with async support
- Create custom exception hierarchy for LLM errors (authentication,
  rate limit, connection, configuration, response errors)
- Refactor adapter factory to use FastAPI Depends() for dependency injection
- Update configuration to support 'openai' mode with API key and model settings
- Add proper HTTP error mapping for all LLM exception types
- Update Dockerfile with default OPENAI_MODEL environment variable
- Update .env.example with OpenAI configuration options

Dockerfile

@@ -9,6 +9,9 @@ RUN pip install --no-cache-dir -r requirements.txt
 # Copy application code
 COPY app/ ./app/
 
+# Default model (API key must be passed at runtime for security)
+ENV OPENAI_MODEL=gpt-4o-mini
+
 # Expose port for Cloud Run
 EXPOSE 8080