Add structured logging to server components

[SongChiYoung]

Currently, there is no logger implemented in the project 😅
To improve debuggability and observability, we need to add structured logging throughout the codebase.

Tasks:
• Add a central logger utility (e.g., using Python logging, structlog, or loguru)
• Integrate logging into key modules:
• server/core.py
• message/ handling (incoming/outgoing logs)
• Include context in logs: session ID, role, message type, etc.
• Optionally, support log level config via env var (e.g., DEBUG / INFO / ERROR)

This will be especially helpful for:
• Tracking request/response flow
• Debugging unexpected behavior
• Auditing OpenAI API calls