feat(mall): live flash-sale page and activity price snapshots

The flash-sale page loads active sessions and their items through the shared
client with live sale price, remaining activity stock, sell-through, and a
countdown, and adds the SKU to the existing cart so checkout resolves the
authoritative price. Payment and order detail tag and render the snapshotted
activity unit price.

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

apps/mall/plugins/api.ts

@@ -21,7 +21,8 @@ type LiveDomain =
   | "invoices"
   | "addresses"
   | "coupons"
-  | "points";
+  | "points"
+  | "flashSales";
 
 /**
  * Explicit per-domain method picks rather than a string allowlist: indexing
@@ -78,6 +79,7 @@ const LIVE_PICKS = {
     listMyRedemptions: a.listMyRedemptions,
     redeemPoints: a.redeemPoints,
   }),
+  flashSales: (a: ApiClient) => ({ listFlashSales: a.listFlashSales }),
 } satisfies Record<LiveDomain, (a: ApiClient) => Partial<ApiClient>>;
 
 const KNOWN_DOMAINS = Object.keys(LIVE_PICKS) as LiveDomain[];
@@ -98,6 +100,7 @@ const DEFAULT_LIVE_DOMAINS: LiveDomain[] = [
   "addresses",
   "coupons",
   "points",
+  "flashSales",
 ];
 
 export default defineNuxtPlugin(() => {