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/features/room/RoomInput.tsx

@@ -314,16 +314,31 @@ export const RoomInput = forwardRef<HTMLDivElement, RoomInputProps>(
       didRestoreDraft.current = true;
       if (msgDraft.length > 0) {
         Transforms.insertFragment(editor, msgDraft);
+      } else {
+        // Jotai draft is empty (page reload) — try localStorage fallback
+        try {
+          const stored = localStorage.getItem(`draft-msg-${roomId}`);
+          if (stored) {
+            const nodes = JSON.parse(stored);
+            if (Array.isArray(nodes) && nodes.length > 0) {
+              Transforms.insertFragment(editor, nodes);
+            }
+          }
+        } catch {
+          // Ignore malformed stored draft
+        }
       }
-    }, [editor, msgDraft]);
+    }, [editor, msgDraft, roomId]);
 
     useEffect(
       () => () => {
         if (!isEmptyEditor(editor)) {
           const parsedDraft = JSON.parse(JSON.stringify(editor.children));
           setMsgDraft(parsedDraft);
+          localStorage.setItem(`draft-msg-${roomId}`, JSON.stringify(parsedDraft));
         } else {
           setMsgDraft([]);
+          localStorage.removeItem(`draft-msg-${roomId}`);
         }
         resetEditor(editor);
         resetEditorHistory(editor);
@@ -463,6 +478,7 @@ export const RoomInput = forwardRef<HTMLDivElement, RoomInputProps>(
       mx.sendMessage(roomId, content as any);
       resetEditor(editor);
       resetEditorHistory(editor);
+      localStorage.removeItem(`draft-msg-${roomId}`);
       setReplyDraft(undefined);
       sendTypingStatus(false);
     }, [mx, roomId, editor, replyDraft, sendTypingStatus, setReplyDraft, isMarkdown, commands]);