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>

apps/Backend/src/ai/new-patient-graph.ts

@@ -5,12 +5,13 @@ import type { ConversationStage } from "./aiHandoffStore";
 // ── Graph state ───────────────────────────────────────────────────────────────
 
 const GraphState = Annotation.Root({
-  message:   Annotation<string>(),
-  stage:     Annotation<string>(),
-  intent:    Annotation<string>(),
-  reply:     Annotation<string>(),
-  language:  Annotation<string>(),
-  nextStage: Annotation<string>(),
+  message:         Annotation<string>(),
+  stage:           Annotation<string>(),
+  intent:          Annotation<string>(),
+  reply:           Annotation<string>(),
+  language:        Annotation<string>(),
+  nextStage:       Annotation<string>(),
+  generalFallback: Annotation<string>(),
 });
 
 type GraphStateType = typeof GraphState.State;
@@ -377,7 +378,7 @@ async function handleSelfPayNode(state: GraphStateType, config: any) {
 
 function transferNode(state: GraphStateType) {
   const lang = state.language || "English";
-  return { reply: transferMsg(lang), nextStage: "done" };
+  return { reply: state.generalFallback || transferMsg(lang), nextStage: "done" };
 }
 
 // ── Graph assembly ────────────────────────────────────────────────────────────
@@ -419,13 +420,14 @@ const graph = new StateGraph(GraphState)
 // ── Public API ────────────────────────────────────────────────────────────────
 
 export async function runNewPatientStep(
-  message:  string,
-  stage:    ConversationStage,
-  language: string,
-  apiKey:   string
+  message:         string,
+  stage:           ConversationStage,
+  language:        string,
+  apiKey:          string,
+  generalFallback  = ""
 ): Promise<{ reply: string; nextStage: ConversationStage }> {
   const result = await graph.invoke(
-    { message, stage, intent: "", reply: "", language, nextStage: "" },
+    { message, stage, intent: "", reply: "", language, nextStage: "", generalFallback },
     { configurable: { apiKey } }
   );
   return {