feat(mall): live group-buying page with open or join intent

The group-buying page lists active activities, the group price against the
catalog price, and each open group with its paid-member count and expiry. A
shopper opens a group or picks one to join; either way the activity SKU goes
into the cart and the intent is carried to checkout, which submits it and hides
the coupon picker for that order. Payment and order detail show the snapshotted
group price.

The group-buying fixtures leave the page; the fixed-data adapter still serves
the domain as the rollback path.

apps/mall/plugins/api.ts

@@ -22,7 +22,8 @@ type LiveDomain =
   | "addresses"
   | "coupons"
   | "points"
-  | "flashSales";
+  | "flashSales"
+  | "groupBuying";
 
 /**
  * Explicit per-domain method picks rather than a string allowlist: indexing
@@ -80,6 +81,9 @@ const LIVE_PICKS = {
     redeemPoints: a.redeemPoints,
   }),
   flashSales: (a: ApiClient) => ({ listFlashSales: a.listFlashSales }),
+  groupBuying: (a: ApiClient) => ({
+    listGroupBuyingActivities: a.listGroupBuyingActivities,
+  }),
 } satisfies Record<LiveDomain, (a: ApiClient) => Partial<ApiClient>>;
 
 const KNOWN_DOMAINS = Object.keys(LIVE_PICKS) as LiveDomain[];
@@ -101,6 +105,7 @@ const DEFAULT_LIVE_DOMAINS: LiveDomain[] = [
   "coupons",
   "points",
   "flashSales",
+  "groupBuying",
 ];
 
 export default defineNuxtPlugin(() => {