feat: label AI-rescheduled appointments and add manual confirm option

- Add movedByAi boolean column to Appointment table (default false)
- reschedule-graph: set movedByAi=true when AI moves an appointment
- PATCH /api/appointments/:id/confirm endpoint clears the movedByAi flag
- Schedule grid: show teal AI badge on appointment cards where movedByAi=true
- Right-click context menu: 'Manually Confirmed' removes the AI badge via the confirm endpoint

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

apps/Backend/src/ai/reschedule-graph.ts

@@ -439,6 +439,7 @@ async function moveAppointment(
     startTime: newStartTime,
     endTime:   newEndTime,
     status:    "scheduled",
+    movedByAi: true,
   } as any);
 
   return "ok";

apps/Backend/src/routes/appointments.ts

@@ -417,6 +417,19 @@ router.put(
   }
 );
 
+// Manually confirm an AI-moved appointment (clears the movedByAi flag)
+router.patch("/:id/confirm", async (req: Request, res: Response): Promise<any> => {
+  try {
+    const id = parseInt(req.params.id);
+    if (isNaN(id)) return res.status(400).json({ message: "Invalid appointment ID" });
+    const updated = await storage.updateAppointment(id, { movedByAi: false } as any);
+    return res.json(updated);
+  } catch (err) {
+    const msg = err instanceof Error ? err.message : String(err);
+    return res.status(500).json({ message: msg });
+  }
+});
+
 // Delete an appointment
 router.delete("/:id", async (req: Request, res: Response): Promise<any> => {
   try {

apps/Frontend/src/pages/appointments-page.tsx

@@ -29,6 +29,8 @@ import {
   MessageSquare,
   Clock,
   ExternalLink,
+  Bot,
+  UserCheck,
 } from "lucide-react";
 import { useToast } from "@/hooks/use-toast";
 import { Calendar } from "@/components/ui/calendar";
@@ -87,6 +89,7 @@ interface ScheduledAppointment {
   patientInsuranceProvider: string | null;
   hasProcedures: boolean;
   hasClaimWithNumber: boolean;
+  movedByAi?: boolean;
   staffId: number;
   date: string | Date;
   startTime: string | Date;
@@ -595,6 +598,7 @@ export default function AppointmentsPage() {
       patientInsuranceProvider,
       hasProcedures: !!(apt as any).hasProcedures,
       hasClaimWithNumber: !!(apt as any).hasClaimWithNumber,
+      movedByAi: !!(apt as any).movedByAi,
       staffId,
       status: apt.status ?? null,
       date: formatLocalDate(apt.date),
@@ -854,6 +858,15 @@ export default function AppointmentsPage() {
         <div className="font-bold truncate flex items-center gap-1">
           <Move className="h-3 w-3" />
           {appointment.patientName}
+          {appointment.movedByAi && (
+            <span
+              className="ml-1 inline-flex items-center gap-0.5 rounded bg-teal-600 px-1 py-0.5 text-[10px] font-semibold text-white leading-none"
+              title="Rescheduled by AI — pending human confirmation"
+            >
+              <Bot className="h-2.5 w-2.5" />
+              AI
+            </span>
+          )}
         </div>
         <div className="truncate">
           {appointment.type?.startsWith("other:")
@@ -977,6 +990,16 @@ export default function AppointmentsPage() {
     console.log(`Opening clinic notes for appointment: ${appointmentId}`);
   };
 
+  const handleManualConfirm = async (appointmentId: number) => {
+    try {
+      await apiRequest("PATCH", `/api/appointments/${appointmentId}/confirm`);
+      queryClient.invalidateQueries({ queryKey: qkAppointmentsDay(formattedSelectedDate) });
+      toast({ title: "Confirmed", description: "AI-moved label removed. Appointment manually confirmed." });
+    } catch (err: any) {
+      toast({ title: "Error", description: err?.message ?? "Failed to confirm appointment.", variant: "destructive" });
+    }
+  };
+
   const handleCheckAllEligibilities = async () => {
     if (!user) {
       toast({
@@ -1596,6 +1619,14 @@ export default function AppointmentsPage() {
               Chat
             </span>
           </Item>
+
+          {/* Manually Confirmed — only relevant for AI-moved appointments */}
+          <Item onClick={({ props }) => handleManualConfirm(props.appointmentId)}>
+            <span className="flex items-center gap-2 text-teal-700">
+              <UserCheck className="h-4 w-4" />
+              Manually Confirmed
+            </span>
+          </Item>
         </Menu>
 
         {/* Main Content  */}