Structured logging with request IDs

[krapfj23]

Summary

Add JSON-structured logging with per-request UUIDs for traceability.

Blocked by

Nothing — this is a starting ticket.

Blocks

Nothing

Steps

1. Install python-json-logger (or use structlog) and add to requirements.txt
2. Create backend/app/middleware/logging.py
3. Add middleware that generates a UUID request_id for every incoming request
4. Attach request_id to all log messages within that request lifecycle
5. Configure JSON log format: {"timestamp", "level", "request_id", "method", "path", "status_code", "duration_ms", "message"}
6. Replace any print() statements with proper logger calls

Acceptance Criteria

• Every request gets a unique request_id
• Logs are structured JSON
• request_id is consistent across all log lines for a single request
• No print() statements remain in active code
• PR body includes Closes #83