web issue fixes

web/app/chat/page.js

@@ -265,6 +265,7 @@ function ChatPage() {
   const isHuman = conversation?.mode === "HUMAN";
   const hasStaff = !!conversation?.staffId;
   const isClosed = conversation?.status === "CLOSED";
+  const hasStaffMessage = messages.some((m) => m.senderId !== user?.id);
 
   const staffStatusLabel = isClosed
     ? "Conversation closed"
@@ -322,7 +323,7 @@ function ChatPage() {
               </button>
             </div>
 
-            {!hasStaff && !isClosed && (
+            {!hasStaff && !hasStaffMessage && !isClosed && (
               <div style={s.waitingBanner}>
                 <span style={s.waitingSpinner} />
                 A support agent will be with you shortly. You can send messages while you wait.