Realtime server: no structured logging, no error categorization, no monitoring

[jasonli2446]

Problem

The realtime server uses console.log / console.error for all logging. In production, this makes debugging and monitoring difficult.

Current State

• All events logged with console.log (connection, disconnection, room lifecycle)
• All errors logged with console.error (generic message + error)
• No structured format (JSON)
• No log levels (debug, info, warn, error)
• No request correlation IDs
• No error categorization (auth vs network vs protocol)
• No metrics collection

What's Needed

1. Structured logging — JSON format with timestamp, level, context
2. Error categorization — Distinguish auth errors, network errors, protocol errors, internal errors
3. Correlation IDs — Track operations across socket events
4. Health metrics — Room count, peer count, producer/consumer count, memory usage
5. Log library — Consider pino or winston for structured logging

Also Missing

• No io.on("error") or io.on("connection_error") handler on the Socket.IO server
• Connection errors are silently lost

Acceptance Criteria

• Replace console.log/error with structured logging library
• Add log levels and error categorization
• Add Socket.IO error event handlers
• Add basic metrics (room/peer counts) to health endpoint
• Add correlation IDs for operation tracking