feat: document title unread count, draft persistence, search date range

E1 - Document title unread count: FaviconUpdater now also sets
     document.title to '(N) Lotus Chat' for mentions, '· Lotus Chat'
     for plain unreads, and 'Lotus Chat' when clear. Reuses the
     existing roomToUnread forEach loop.

E2 - Draft persistence across reloads: on room unmount, unsent message
     is written to localStorage as 'draft-msg-<roomId>'. On mount, if
     the Jotai atom is empty (page reload), the localStorage draft is
     restored. Cleared on send. Uses the existing Slate node JSON format.

E5 - Search date range filter: new DateRangeButton in SearchFilters
     with From/To date inputs in a PopOut. Dates stored as epoch ms in
     ?fromTs=&toTs= URL params. Passed to Matrix /search as from_ts /
     to_ts filter fields (valid spec fields, cast via 'as any' since
     SDK types don't include them yet).

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

src/app/pages/client/ClientNonUIFeatures.tsx

@@ -56,22 +56,26 @@ function FaviconUpdater() {
   const roomToUnread = useAtomValue(roomToUnreadAtom);
 
   useEffect(() => {
-    let notification = false;
-    let highlight = false;
+    let totalNotif = 0;
+    let totalHighlight = 0;
     roomToUnread.forEach((unread) => {
-      if (unread.total > 0) {
-        notification = true;
-      }
-      if (unread.highlight > 0) {
-        highlight = true;
-      }
+      totalNotif += unread.total;
+      totalHighlight += unread.highlight;
     });
 
-    if (notification) {
-      setFavicon(highlight ? LogoHighlightSVG : LogoUnreadSVG);
+    if (totalNotif > 0) {
+      setFavicon(totalHighlight > 0 ? LogoHighlightSVG : LogoUnreadSVG);
     } else {
       setFavicon(LogoSVG);
     }
+
+    if (totalHighlight > 0) {
+      document.title = `(${totalHighlight}) Lotus Chat`;
+    } else if (totalNotif > 0) {
+      document.title = `· Lotus Chat`;
+    } else {
+      document.title = 'Lotus Chat';
+    }
   }, [roomToUnread]);
 
   return null;