fix: clinicId on all appointment paths + startedAt on call records

- AI chat book_appointment tool: accepts optional clinicId
- Widget booking: passes clinicId from request
- LiveKit agent: passes clinicId from doctor context if available
- Dispose endpoint: sets startedAt/endedAt on outbound call records
  (computed from durationSec). Fixes null timestamps in call history.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/livekit-agent/agent.ts

@@ -128,6 +128,7 @@ const bookAppointment = llm.tool({
                     doctorName: doctor?.name ?? doctorName ?? 'To be assigned',
                     department,
                     reasonForVisit: reason,
+                    ...((doctor as any)?.clinicId ? { clinicId: (doctor as any).clinicId } : {}),
                 },
             },
         );