Structured logging with correlation IDs

[howwohmm]

Problem

All logging is `print()` statements. No log levels, no structured format, no correlation IDs. At 1K DAU, debugging from `docker logs` is impossible — can't trace a request through transcript fetch → LLM call → email scheduling.

Solution

• Replace all `print()` with Python `logging` module
• Use structured JSON format (for log aggregation)
• Add request correlation IDs (middleware that sets a request ID)
• Log levels: DEBUG for verbose, INFO for operations, WARNING for degraded, ERROR for failures

Files

• All `.py` files — replace `print()` with `logger.info()` etc.
• `main.py` — add correlation ID middleware

Acceptance Criteria

• All print statements replaced with structured logging
• Each request has a traceable correlation ID
• Log output is JSON-formatted
• Log levels used appropriately