Refactor Server-Side Logging

- **Remove external logs**: Find and remove all explicit logging statements (e.g., `console.log`) outside of `websocket.ts`.
- **Clean up `websocket.ts` logs**:
- Remove duplicate console calls (e.g., `console.error` next to `logger.error`).
- Standardize log formatting for readability.
- **Reduce noise & protect data**: Remove or downgrade high-frequency connection informational logs (e.g., "Upgrade request received") and ensure no sensitive payloads or tokens are logged.

- Analyze if it would be better to handle the log file and console separately