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/paths.ts

@@ -33,6 +33,8 @@ export type _SearchPathSearchParams = {
   order?: string;
   rooms?: string;
   senders?: string;
+  fromTs?: string;
+  toTs?: string;
 };
 export const _SEARCH_PATH = 'search/';