feat(catalog): update the catalog live after an import, no page refresh

Organising imports, the Studio furni batch, the catalog totals and the
"import from a source" stats all used to need a full page reload, or at
best a router.refresh() that re-rendered the whole admin route, before
anything on screen reflected what the import had just written.

- live-catalog-merge.ts (new): pure tree and total arithmetic. Applies a
  delta of created pages, added offers and moved offers, recomputes depth
  for the touched subtree, bumps parent child counts and the item totals.
  Returns the input untouched when a delta is empty, so subscribers can
  bail out instead of re-rendering. Depth resolution tolerates a parent
  cycle in a dirty DB and still terminates, matching getTreeFlat.
- use-live-catalog.ts (new): one module-level store exposed through
  useSyncExternalStore, so every consumer shares a single instance without
  threading a provider through the admin layout. Deltas only apply to the
  "normal" catalog, so public and public_handlers trees stay separate.
  seedCatalogTotals() takes the first server value per mode and never
  overwrites it afterwards, so a later hard render cannot make the header
  totals jump backwards.
- actions/catalog.ts: organizeImportFurni now reports each group through
  the new OrganizedPageChange, carrying parentId, pageLayout, the icon,
  isNew and the per-source movedFrom counts, so the client can fold the
  result into the tree without reading the page back.
- organize-imports-dialog.tsx: drops useRouter and router.refresh(); the
  response is applied as a delta the moment the run finishes.
- studio-client.tsx: reads the tree from the store instead of freezing it
  with useState(initialTree), loads it on mount when empty, and refreshes
  it once a batch import settles. The batch is server-side and derives its
  import pages from furnidata, so that one path re-reads the tree via
  GET /api/admin/catalog/tree?mode=full rather than trusting the delta.
- studio/furni/page.tsx: stops calling getTreeFlat() and no longer passes
  initialTree; the store is the single source of truth for the rail.
- import-clone-client.tsx: tracks which items are already present, so
  present and clonable update per cloned row instead of only at the end.
- catalog-manager-dialog.tsx: seeds the totals once and renders the live
  values, so the header reflects an import that just ran.
- e2e/ui/fixtures/entry.tsx: drops the removed initialTree prop.

src/components/admin/studio/studio-client.tsx

@@ -63,11 +63,15 @@ import {
 	SelectValue,
 } from "@/components/ui/select";
 import { Switch } from "@/components/ui/switch";
+import {
+	ensureCatalogTreeLoaded,
+	refreshCatalogTree,
+	useLiveCatalog,
+} from "@/features/catalog/client/use-live-catalog";
 import { adminFetch } from "@/lib/admin-fetch";
 import type { FurniImportSource } from "@/lib/habbo-gamedata-hotel";
 import { readSseStream } from "@/lib/sse-client";
 import { cn } from "@/lib/utils";
-import type { TreeNode } from "@/types/catalog";
 import { BatchProgress } from "./batch-progress";
 import { CatalogRail } from "./catalog-rail";
 import { CheckboxDot } from "./checkbox-dot";
@@ -169,12 +173,10 @@ const TABLE_ROW_H = 40;
 export function StudioClient({
 	actorId,
 	source,
-	initialTree,
 	defaultTranslate,
 }: {
 	actorId?: number;
 	source: FurniImportSource;
-	initialTree: TreeNode[];
 	defaultTranslate: boolean;
 }) {
 	const [review, setReview] = useState<{
@@ -191,12 +193,14 @@ export function StudioClient({
 		actorId,
 	);
 	const [preparingReview, setPreparingReview] = useState(false);
-	// Catalog tree
-	const [tree] = useState<TreeNode[]>(initialTree);
+	// Catalog tree — read from the live store so pages created by an import show
+	// up without re-rendering the route.
+	const tree = useLiveCatalog().tree;
 	const [selectedPage, setSelectedPage] = useState<number | null>(null);
 	const [railOpen, setRailOpen] = useState(false);
 	useEffect(() => {
 		setRailOpen(window.matchMedia("(min-width: 1024px)").matches);
+		void ensureCatalogTreeLoaded();
 	}, []);
 
 	// Search & list
@@ -957,6 +961,10 @@ export function StudioClient({
 			setBatchCancelling(false);
 			setSelected(new Set());
 			fetchStats();
+			// The importers derive their "Imported Furniture" category pages from
+			// furnidata, so the client cannot predict which pages appeared. Pull the
+			// tree over the API instead of re-rendering the route.
+			void refreshCatalogTree();
 			if (!batchDoneRef.current) markBatchDone();
 		}
 	}