Refactor startMeeting and endMeeting functions to refetch appointment details

Update the startMeeting and endMeeting functions in appointments.ts to ensure they return the latest appointment state by refetching details from the API. This change addresses the issue of receiving outdated appointment data and improves the accuracy of meeting management functionality.

lib/actions/appointments.ts

@@ -768,7 +768,9 @@ export async function startMeeting(
     throw new Error(extractErrorMessage(data as unknown as ApiError));
   }
 
-  return (data as AppointmentResponse).appointment || data;
+  // The API returns { action, metadata, recording_url }, not an Appointment
+  // So we need to refetch the appointment to get the updated state
+  return await getAppointmentDetail(id);
 }
 
 export async function endMeeting(id: string): Promise<Appointment> {
@@ -790,5 +792,7 @@ export async function endMeeting(id: string): Promise<Appointment> {
     throw new Error(extractErrorMessage(data as unknown as ApiError));
   }
 
-  return (data as AppointmentResponse).appointment || data;
+  // The API returns a response object, not an Appointment
+  // So we need to refetch the appointment to get the updated state
+  return await getAppointmentDetail(id);
 }