Fix category-slot matching: identity by linkUrl slug, not array position

The homepage category carousel and installments highlights matched
slot.images[i] to categoryList[i] by array index, assuming the business's
CMS upload order lines up with this site's own category sort order. It
doesn't - live data showed a laptop photo landing on "موبایل" and "لوازم
برقی" appearing on the site despite no photo ever being uploaded for it,
purely from index luck. titleFa isn't reliable either: the same laptop image
was titled "تبلت" in the CMS, contradicting its own linkUrl.

Fix: resolve each image's category from the `category` query param on its
own linkUrl (categorySlugFromLinkUrl() in slug.ts, matched against
ApiCategory.slug via the new findNodeBySlug()). The homepage carousel is now
fully slot-driven - it iterates slot.images (in the CMS's own sortOrder) and
simply omits any category with no matching image, per explicit product
direction, rather than falling back to a placeholder. Installments keeps its
curated HIGHLIGHT_IDS list with a placeholder for uncovered categories,
since that page always shows the same fixed set, but now uses the same
identity-based lookup instead of position.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

src/lib/categoryTree.ts

@@ -35,6 +35,15 @@ export function findNode(nodes: CategoryNode[], id: string): CategoryNode | unde
   return undefined;
 }
 
+export function findNodeBySlug(nodes: CategoryNode[], slug: string): CategoryNode | undefined {
+  for (const node of nodes) {
+    if (node.slug === slug) return node;
+    const hit = findNodeBySlug(node.children, slug);
+    if (hit) return hit;
+  }
+  return undefined;
+}
+
 // Products are filed against leaf categories, so a parent like "لوازم جانبی"
 // matches almost nothing on its own — a carousel for it has to ask for the
 // whole subtree. Capped for the homepage's small carousels; a full category

src/lib/slug.ts

@@ -22,3 +22,18 @@ export function categoryHref(id: string, nameFa?: string | null, name?: string |
 export function blogHref(id: string, title?: string | null): string {
   return `/blog/${id}/${faSlug(title)}`;
 }
+
+// Static-image-slot items carry a business-picked linkUrl like
+// "https://moalem.shop/products?category=mobile" — the `category` query
+// param is the DB slug (ApiCategory.slug), the one reliable way to identify
+// which category an uploaded photo is actually for. Position in the list
+// and the item's own titleFa are NOT reliable — see AGENTS.md "Static-image
+// slots" for the real mismatch this was built to fix.
+export function categorySlugFromLinkUrl(linkUrl: string | null | undefined): string | null {
+  if (!linkUrl) return null;
+  try {
+    return new URL(linkUrl).searchParams.get("category");
+  } catch {
+    return null;
+  }
+}