feat: persist AI conversation state in DB and fix LangGraph flow bugs

- Replace in-memory Maps in aiHandoffStore with DB-backed async functions
  using new patient_conversation table (stage + aiHandoff per patient)
- Add afterHoursEnabled to ai_settings table (persists across restarts)
- Fix runtime crash in reschedule-graph: mon/tue/wed variables were out
  of scope in the next-week fallback branch (ReferenceError)
- Wire rescheduleGreeting and generalFallback chat templates through to
  LangGraph nodes so user-configured messages take effect
- Add otherNode to reminder-graph to handle unclassified patient replies
  (e.g. "I want another appointment") and route to booking flow
- Fetch chatTemplates once per webhook request instead of per stage

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

packages/db/shared/schemas/variants/input/Patient.input.ts

@@ -30,7 +30,8 @@ export const PatientInputSchema = z.object({
     groups: z.array(z.unknown()),
     payment: z.array(z.unknown()),
     communications: z.array(z.unknown()),
-    documents: z.array(z.unknown())
+    documents: z.array(z.unknown()),
+    conversation: z.unknown().optional().nullable()
 }).strict();
 
 export type PatientInputType = z.infer<typeof PatientInputSchema>;