feat(rooms): Mark as Unread (MSC2867) + Low Priority rooms

Two Matrix protocol gaps (Phase A), gate-green (683 tests):
- Mark as Unread: m.marked_unread room account data (+ com.famedly.marked_unread
  fallback), a new markedUnreadAtom binder that seeds from account data and
  clears on our own read receipt (MSC2867). RoomNavItem gains Mark as Unread /
  Read menu items and lights the row dot for a marked room. Tested.
- Low Priority: m.lowpriority room tag mirroring favourites — a context-menu
  toggle (mutually exclusive with Favorite) and a collapsed Low Priority
  category sorted to the bottom of the Home room list.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/app/pages/client/home/Home.tsx

@@ -223,6 +223,7 @@ const factoryRoomIdByUnread =
 
 const DEFAULT_CATEGORY_ID = makeNavCategoryId('home', 'room');
 const FAVORITES_CATEGORY_ID = makeNavCategoryId('home', 'favorite');
+const LOW_PRIORITY_CATEGORY_ID = makeNavCategoryId('home', 'lowpriority');
 export function Home() {
   const mx = useMatrixClient();
   useNavToActivePathMapper('home');
@@ -261,18 +262,21 @@ export function Home() {
   const roomToUnread = useAtomValue(roomToUnreadAtom);
   const [sortMenuAnchor, setSortMenuAnchor] = useState<RectCords>();
 
-  const { favoriteRooms, otherRooms } = useMemo(() => {
+  const { favoriteRooms, lowPriorityRooms, otherRooms } = useMemo(() => {
     const favs: string[] = [];
+    const low: string[] = [];
     const others: string[] = [];
     rooms.forEach((rId) => {
       const room = mx.getRoom(rId);
       if (room?.tags?.['m.favourite']) {
         favs.push(rId);
+      } else if (room?.tags?.['m.lowpriority']) {
+        low.push(rId);
       } else {
         others.push(rId);
       }
     });
-    return { favoriteRooms: favs, otherRooms: others };
+    return { favoriteRooms: favs, lowPriorityRooms: low, otherRooms: others };
   }, [mx, rooms]);
 
   const sortedFavoriteRooms = useMemo(() => {
@@ -297,6 +301,28 @@ export function Home() {
     });
   }, [mx, sortedFavoriteRooms, filterQuery]);
 
+  const sortedLowPriorityRooms = useMemo(() => {
+    const isClosed = closedCategories.has(LOW_PRIORITY_CATEGORY_ID);
+    const items = Array.from(lowPriorityRooms).sort(
+      isClosed ? factoryRoomIdByActivity(mx) : factoryRoomIdByAtoZ(mx),
+    );
+    if (isClosed) {
+      return items.filter((rId) => roomsWithUnreadSet.has(rId) || rId === selectedRoomId);
+    }
+    return items;
+  }, [mx, lowPriorityRooms, closedCategories, roomsWithUnreadSet, selectedRoomId]);
+
+  const filteredLowPriorityRooms = useMemo(() => {
+    if (!filterQuery.trim()) return sortedLowPriorityRooms;
+    const query = filterQuery.toLowerCase();
+    const localNames = getLocalRoomNamesContent(mx);
+    return sortedLowPriorityRooms.filter((rId) => {
+      const localName = localNames.rooms[rId];
+      const matrixName = mx.getRoom(rId)?.name ?? '';
+      return (localName ?? matrixName).toLowerCase().includes(query);
+    });
+  }, [mx, sortedLowPriorityRooms, filterQuery]);
+
   const sortedRooms = useMemo(() => {
     const isClosed = closedCategories.has(DEFAULT_CATEGORY_ID);
     let comparator: (a: string, b: string) => number;
@@ -349,6 +375,13 @@ export function Home() {
     overscan: 10,
   });
 
+  const lowVirtualizer = useVirtualizer({
+    count: filteredLowPriorityRooms.length,
+    getScrollElement: () => scrollRef.current,
+    estimateSize: () => 38,
+    overscan: 10,
+  });
+
   const handleCategoryClick = useCategoryHandler(setClosedCategories, (categoryId) =>
     closedCategories.has(categoryId),
   );
@@ -638,6 +671,43 @@ export function Home() {
                 })}
               </div>
             </NavCategory>
+            {lowPriorityRooms.length > 0 && (
+              <NavCategory>
+                <NavCategoryHeader>
+                  <RoomNavCategoryButton
+                    closed={closedCategories.has(LOW_PRIORITY_CATEGORY_ID)}
+                    data-category-id={LOW_PRIORITY_CATEGORY_ID}
+                    onClick={handleCategoryClick}
+                  >
+                    Low Priority
+                  </RoomNavCategoryButton>
+                </NavCategoryHeader>
+                <div style={{ position: 'relative', height: lowVirtualizer.getTotalSize() }}>
+                  {lowVirtualizer.getVirtualItems().map((vItem) => {
+                    const roomId = filteredLowPriorityRooms[vItem.index];
+                    const room = mx.getRoom(roomId);
+                    if (!room) return null;
+                    return (
+                      <VirtualTile
+                        virtualItem={vItem}
+                        key={roomId}
+                        ref={lowVirtualizer.measureElement}
+                      >
+                        <RoomNavItem
+                          room={room}
+                          selected={selectedRoomId === roomId}
+                          linkPath={getHomeRoomPath(getCanonicalAliasOrRoomId(mx, roomId))}
+                          notificationMode={getRoomNotificationMode(
+                            notificationPreferences,
+                            room.roomId,
+                          )}
+                        />
+                      </VirtualTile>
+                    );
+                  })}
+                </div>
+              </NavCategory>
+            )}
           </Box>
         </PageNavContent>
       )}