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.types.ts

@@ -15,6 +15,7 @@ export type WidgetInitResponse = {
 export type WidgetBookRequest = {
     departmentId: string;
     doctorId: string;
+    clinicId?: string;
     scheduledAt: string;
     patientName: string;
     patientPhone: string;