BE-042: PUT /sessions/{id}/start — transition to live

Track: 1 — MVP
Section: 1.12 Live Session Lifecycle
Status: [ ] Todo
Repo: backend-api
Branch: feature/BE-042-start-session

Done When

Only session owner (coach) can start. Status changes "scheduled" → "live". started_at set to now. Starting already-live session returns 409

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