Epic: Enhanced structured logging system

[psschwei]

Description:
Enhance the existing FancyLogger to integrate with the rest of the observability stack. This enables log-trace correlation, structured context propagation, and flexible output destinations while preserving the existing API.

Current State:

• FancyLogger in mellea/core/utils.py uses Python's built-in logging module
• Custom formatters: CustomFormatter (colored console), JsonFormatter (JSON serialization)
• Optional RESTHandler for HTTP webhook logging (only active if FLOG env var set)
• No correlation with distributed tracing (no trace_id/span_id injection)
• No contextvars integration for async flows
• Used in 13+ files across backends, requirements, components, and sampling strategies

Acceptance Criteria:

• Automatic trace_id/span_id injection from OpenTelemetry
• Context propagation via contextvars (session_id, request_id, model_id)
• Multiple output sinks (stdout, file, OTLP logs)
• Existing FancyLogger API preserved

[ajbozarth]

I'll be picking up this epic in addition to my work on #443 in order to get a MVP of OTLP integration into the next release. I've shared the detailing in #460 (comment)

[AngeloDanducci]

All subtasks complete.