feat(mall): read the store directory from the API

Wave 5: the store directory, store home and product-page store card stop reading
MOCK_STORES, and the payment and order surfaces name their shop.

- a `shop_profiles` table beside `shops`, so the identity model both consoles
  consume is untouched, with a public `GET /api/shops` and `GET /api/shops/{slug}`
  and an admin `PUT /api/admin/shops/{id}/profile`
- a shop with no profile is still listed, with the fields absent rather than
  invented; the pages guard every block, and a missing logo renders an
  initial-letter placeholder
- `scripts/seed-demo.mjs` upserts a profile per demo shop, since profiles hang
  off shops that script creates
- payment and order pages resolve shop ids to names from one cached shop read,
  retiring the generic "Shop" label
- three things went rather than being faked, following the wave-1 precedent:
  `distanceKm` and its sort (no geo model), the store home's sales/comments
  sorts, and its "best sellers" rail (no sales model)
- `lowestSku` moved out of the fixed-data module into `apps/mall/utils/product.ts`
  and re-exported, so live pages stop importing the mock module for a pure
  helper

Verified: 28 backend tests green including five new shop tests; all three
frontends build; the directory, store home, store card and order cards all render
real data with no distance or sales claims; the fixed-data rollback still renders
the store surfaces with the backend stopped.

Note: `nuxt build` does not typecheck in this repo (no `typescript.typeCheck`,
no `vue-tsc`), which AGENTS.md implies it does. A re-export used here created no
local binding and broke internal callers at runtime while the build stayed green;
`docs/TBD-migrate-wave.md` records the gap.

OpenSpec change: openspec/changes/replace-mock-api-wave-5

apps/mall/mock/api.ts

@@ -15,6 +15,7 @@ import type {
   Order,
   Product,
   Shipment,
+  ShopProfile,
   User,
 } from "@vmall/shared";
 import {
@@ -87,6 +88,28 @@ function unsupported(): never {
   throw new ApiError(501, "MOCK_UNSUPPORTED", "This admin/shop endpoint is not part of the mall mock.");
 }
 
+type MockStoreRecord = NonNullable<ReturnType<typeof storeById>>;
+
+/** Mock stores carry a nested `rate`; the API exposes flat score fields. */
+function toShopProfile(store: MockStoreRecord): ShopProfile {
+  return {
+    id: store.id,
+    slug: store.slug,
+    name: store.name,
+    company: store.company,
+    region: store.region,
+    address: store.address,
+    logo: store.logo,
+    banner: store.banner,
+    notice: store.notice,
+    after_sale: store.afterSale,
+    score_rating: store.rate.score,
+    score_agreement: store.rate.agree,
+    score_service: store.rate.service,
+    score_speed: store.rate.speed,
+  };
+}
+
 
 function skuIndex(): Record<string, { product: Product; skuId: string }> {
   const index: Record<string, { product: Product; skuId: string }> = {};
@@ -352,6 +375,13 @@ export function createMockApi(): ApiClient {
         })),
       }),
 
+    listShops: (): Promise<ShopProfile[]> => Promise.resolve(MOCK_STORES.map(toShopProfile)),
+    getShop: (slug) => {
+      const store = storeById(slug);
+      if (!store) return Promise.reject(new ApiError(404, "NOT_FOUND", "Shop not found"));
+      return Promise.resolve(toShopProfile(store));
+    },
+
     shop: {
       getMyShop: () => unsupported(),
       listMyProducts: () => unsupported(),
@@ -381,6 +411,7 @@ export function createMockApi(): ApiClient {
       setRate: () => unsupported(),
       getContent: () => unsupported(),
       replaceContent: () => unsupported(),
+      setShopProfile: () => unsupported(),
     },
   };
 }