feat: auto-populate patient fields from member ID on eligibility page

When a member ID is typed on the insurance eligibility page, debounced
lookup fills in date of birth, first name, and last name if the patient
already exists in the database.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

apps/Backend/src/ai/aiHandoffStore.ts

@@ -72,6 +72,12 @@ export function startNewPatientConversation(userId: number, patientId: number):
   stageStore.set(convKey(userId, patientId), "new_patient_greeted");
 }
 
+// Called when office sends a reschedule greeting — patient's next reply enters
+// the reschedule flow.
+export function startRescheduleConversation(userId: number, patientId: number): void {
+  stageStore.set(convKey(userId, patientId), "asked_reschedule_confirm");
+}
+
 // ── Pending reschedule data ───────────────────────────────────────────────────
 // Holds the confirmed new date while AI waits for a time-slot answer.