fix(catalog): keep the live catalog truthful after every import path

The live catalog store only covered part of the import surface. A durable
job settled, a sync queue drained, a .nitro upload or a clone run left the
Studio rail and the stats bar showing pre-import numbers until the page was
reloaded, and the Catalog Manager kept a second tree that never saw writes
made elsewhere in the session.

Every one of those paths now pulls the tree again, and the refresh carries
the totals with it: importing writes catalog rows server-side, so the counts
the store holds were stale for the rest of the session.

- refreshCatalogTree shares one request between concurrent callers and queues
  a single follow-up read when a write lands mid-flight, so a burst of edits
  costs at most one extra read.
- useFurnitureJobs treats its first payload as a baseline, so a page load no
  longer replays every past import as "just settled", and hands the settled
  jobs to the callback.
- The Catalog Manager pushes its own mutations into the store and re-reads its
  active tab when the store changes.
- The 30s unstable_cache on the admin totals is now tagged and invalidated from
  every catalog write, including the import worker, so it no longer survives an
  import even across a hard reload.

Co-Authored-By: Claude Opus 4.8 (1M context) <[email protected]>

src/components/admin/catalog-manager/catalog-manager-dialog.tsx

@@ -13,6 +13,7 @@ import type { CatalogSelection } from "@/features/catalog/client/catalog-selecti
 import { useCatalogNavigation } from "@/features/catalog/client/use-catalog-navigation";
 import { useLatestRequest } from "@/features/catalog/client/use-latest-request";
 import {
+	refreshCatalogTree,
 	seedCatalogTotals,
 	useLiveCatalog,
 } from "@/features/catalog/client/use-live-catalog";
@@ -271,6 +272,16 @@ function CatalogManagerInner({
 		}
 	}, [dispatch, catQs, rootRequests]);
 
+	/**
+	 * A page created, moved or deleted here changes the tree the Studio rail and
+	 * the stats bar read from the live store. Refreshing it here keeps both views
+	 * truthful without a route re-render; the store coalesces bursts of edits.
+	 */
+	const onTreeMutation = useCallback(() => {
+		void loadRootPages();
+		void refreshCatalogTree();
+	}, [loadRootPages]);
+
 	// Seed once on opening, then refresh independently of category selection.
 	useEffect(() => {
 		if (!open) return;
@@ -504,7 +515,7 @@ function CatalogManagerInner({
 						activeTabId={state.activeTabId}
 						selectedPageId={state.selectedPageId}
 						onSelectPage={handleSelectPage}
-						onTreeMutation={loadRootPages}
+						onTreeMutation={onTreeMutation}
 						nodeUpdate={null}
 					/>
 				</div>