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feat(ai): trace_context 구현 — 문서에만 있던 함수를 실제로 만든다 #190

Job	Run time
Backend (Core, Spring)	1m 2s
Frontend (lint · types · test · build)	59s
Infra (ops 스크립트)	19s
RealTime (Go)	48s
AI (FastAPI/LangChain)	27s
	3m 35s