v0.6.5 various updates

frontend/src/pages/Chat.jsx

@@ -190,11 +190,20 @@ export default function Chat() {
     setUnreadGroups(prev => { const next = new Map(prev); next.delete(id); return next; });
   };
 
-  // Update page title with total unread badge count
+  // Update page title AND PWA app badge with total unread count
   useEffect(() => {
     const totalUnread = [...unreadGroups.values()].reduce((a, b) => a + b, 0);
+    // Strip any existing badge prefix to get the clean base title
     const base = document.title.replace(/^\(\d+\)\s*/, '');
     document.title = totalUnread > 0 ? `(${totalUnread}) ${base}` : base;
+    // PWA app icon badge (Chrome/Edge desktop + Android, Safari 16.4+)
+    if ('setAppBadge' in navigator) {
+      if (totalUnread > 0) {
+        navigator.setAppBadge(totalUnread).catch(() => {});
+      } else {
+        navigator.clearAppBadge().catch(() => {});
+      }
+    }
   }, [unreadGroups]);
 
   const activeGroup = [