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/message-search/MessageSearch.tsx

@@ -33,6 +33,8 @@ const useSearchPathSearchParams = (searchParams: URLSearchParams): _SearchPathSe
       order: searchParams.get('order') ?? undefined,
       rooms: searchParams.get('rooms') ?? undefined,
       senders: searchParams.get('senders') ?? undefined,
+      fromTs: searchParams.get('fromTs') ?? undefined,
+      toTs: searchParams.get('toTs') ?? undefined,
     }),
     [searchParams],
   );
@@ -193,6 +195,8 @@ export function MessageSearch({
       order: searchPathSearchParams.order ?? SearchOrderBy.Recent,
       rooms: searchParamRooms ?? defaultRooms,
       senders: searchParamsSenders ?? senders,
+      fromTs: searchPathSearchParams.fromTs ? Number(searchPathSearchParams.fromTs) : undefined,
+      toTs: searchPathSearchParams.toTs ? Number(searchPathSearchParams.toTs) : undefined,
     };
   }, [searchPathSearchParams, searchParamRooms, searchParamsSenders, rooms, senders]);
 
@@ -235,6 +239,8 @@ export function MessageSearch({
       msgSearchParams.order,
       msgSearchParams.rooms,
       msgSearchParams.senders,
+      msgSearchParams.fromTs,
+      msgSearchParams.toTs,
     ],
     queryFn: ({ pageParam }) => searchMessages(pageParam),
     initialPageParam: '',
@@ -329,6 +335,20 @@ export function MessageSearch({
     [searchParamsSenders, handleSelectedSendersChange],
   );
 
+  const handleDateRangeChange = useCallback(
+    (fromTs?: number, toTs?: number) => {
+      setSearchParams((prevParams) => {
+        const p = new URLSearchParams(prevParams);
+        p.delete('fromTs');
+        p.delete('toTs');
+        if (fromTs) p.append('fromTs', String(fromTs));
+        if (toTs) p.append('toTs', String(toTs));
+        return p;
+      });
+    },
+    [setSearchParams],
+  );
+
   const lastVItem = vItems[vItems.length - 1];
   const lastVItemIndex: number | undefined = lastVItem?.index;
   const lastGroupIndex = groups.length - 1;
@@ -378,6 +398,9 @@ export function MessageSearch({
           onOrderChange={handleOrderChange}
           selectedSenders={searchParamsSenders}
           onSelectedSendersChange={handleSelectedSendersChange}
+          fromTs={msgSearchParams.fromTs}
+          toTs={msgSearchParams.toTs}
+          onDateRangeChange={handleDateRangeChange}
         />
       </Box>