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/widget/widget.service.ts

@@ -204,6 +204,7 @@ export class WidgetService {
                 department: req.departmentId,
                 reasonForVisit: req.chiefComplaint ?? '',
                 patientId,
+                ...(req.clinicId ? { clinicId: req.clinicId } : {}),
             } },
             this.auth,
         );