feat(mall): serve catalog and currency from the live API

Wave 1 of replacing the fixed-data mock adapter. The mall now selects its API
adapter per domain, with catalog and currency served live while auth, cart,
orders, shipments and invoices stay on fixed data.

Backend:
- seed the 6 x 2 x 2 category tree as reference data (migration 0005). The API
  exposes no category write route, so this cannot come from the seed script
- filter public product listing by the category subtree with a recursive CTE,
  matching the mock's existing behaviour instead of exact-match
- add sort=price with order=asc|desc, validated by hand so an unsupported value
  returns the project's ApiError 400 shape rather than axum's own rejection

Mall:
- replace the all-or-nothing mockApi boolean with a liveDomains list composed
  through a typed per-domain pick map
- source home floors, the category menu, search and product detail from the
  catalog API; banners, promos, quick links, store card and comment/coupon
  content stay local display-only content
- drop the brand facet and the sales/comments sorts: no backend model backs them
- fix salesOf/commentCountOf, which parsed digits out of the product id and so
  rendered "NaN sold" for live UUID ids; they now hash the id

Seed: 24 products across 4 shops, idempotent on re-run.

Note: the mall defaults to a live catalog, so pnpm dev:mall now expects the API
to be running; set NUXT_PUBLIC_LIVE_DOMAINS to an empty array for all-mock work.

OpenSpec change: openspec/changes/replace-mock-api-wave-1

apps/mall/pages/goods/[id].vue

@@ -1,11 +1,14 @@
 <script setup lang="ts">
 import { t as pick } from "@vmall/shared";
-import type { Category, Sku } from "@vmall/shared";
+import type { Category, Product, Sku } from "@vmall/shared";
 import {
-  MOCK_CATEGORIES,
+  MOCK_COUPONS,
+  MOCK_STORES,
+  commentStats,
+  commentsFor,
   lowestSku,
-  productDetail,
   salesOf,
+  storeById,
 } from "~/mock/data";
 import { useCartStore } from "~/stores/cart";
 
@@ -21,8 +24,47 @@ const routeId = computed(() => {
   const value = route.params.id;
   return Array.isArray(value) ? value[0] ?? "" : value ?? "";
 });
-const detail = computed(() => productDetail(routeId.value));
-const product = computed(() => detail.value?.product ?? null);
+// One request key for the whole page: the ranking rail must be derived from the
+// product that was just fetched, and chaining two useAsyncData calls left the
+// second handler running before the first had data.
+const { data: pageData } = await useAsyncData(
+  "product-detail",
+  async () => {
+    const current = await $api.getProduct(routeId.value);
+    // The rail uses live catalogue products so its links resolve; the store
+    // card, comments and coupons stay local display-only content (non-goals).
+    // Store best sellers, mirroring the mock's salesRankFor(shopId). Ranking by
+    // category would empty the rail for any product alone in its leaf category.
+    const siblings = await $api.listProducts({
+      shop_id: current.shop_id,
+      per_page: 6,
+    });
+    return {
+      product: current,
+      related: siblings.items.filter((item) => item.id !== current.id).slice(0, 5),
+    };
+  },
+  { watch: [routeId], default: () => null },
+);
+
+const product = computed(() => pageData.value?.product ?? null);
+const related = computed<Product[]>(() => pageData.value?.related ?? []);
+
+const detail = computed(() => {
+  const current = product.value;
+  if (!current) return null;
+  return {
+    product: current,
+    store: storeById(current.shop_id) ?? MOCK_STORES[0],
+    comments: commentsFor(current.id),
+    commentStats: commentStats(current.id),
+    coupons: MOCK_COUPONS,
+    salesRank: related.value,
+  };
+});
+
+/// Display-only sales figure; `salesOf` hashes the id so it is safe for UUIDs.
+
 const store = computed(() => detail.value?.store ?? null);
 const selectedAttributes = reactive<Record<string, string>>({});
 const quantity = ref(1);
@@ -76,7 +118,10 @@ const marketPrice = computed(() => {
 });
 const currentImage = computed(() => product.value?.images[galleryIndex.value] ?? product.value?.images[0] ?? "/mock/product-1.svg");
 
-const categoryById = (id: string): Category | undefined => MOCK_CATEGORIES.find((category) => category.id === id);
+// Shared with the shell's category menu, so the tree is not refetched.
+const { data: categories } = await useAsyncData("shell-categories", () => $api.listCategories());
+const categoryById = (id: string): Category | undefined =>
+  (categories.value ?? []).find((category) => category.id === id);
 const categoryPath = computed(() => {
   const path: Category[] = [];
   let current = product.value?.category_id ? categoryById(product.value.category_id) : undefined;