chore: final verification fixes for sitemap reliability

- Replace invalid revalidate export with unstable_cache in sitemap.ts
- Add revalidateTag('sitemap', 'default') to on-demand revalidation endpoint
- Fix test assertions to match /game/ URL path

app/sitemap.ts

@@ -1,19 +1,36 @@
 import type { MetadataRoute } from "next"
+import { unstable_cache } from "next/cache"
 import { buildStaticEntries } from "@/lib/sitemap/build-static-entries"
 import { fetchDynamicEntries } from "@/lib/sitemap/fetch-dynamic-entries"
 
+const REVALIDATE_SECONDS = Number(process.env.SITEMAP_REVALIDATE_SECONDS) || 3600
+
 /**
- * ISR revalidation interval for the sitemap.
+ * Caches the full sitemap generation with time-based revalidation.
  *
- * Instead of `force-dynamic`, we use ISR so the sitemap is cached and
- * regenerated in the background. This keeps response times fast for
- * crawlers while still reflecting recent changes on the site.
+ * Instead of `force-dynamic` (which hits the DB on every crawler request),
+ * we use `unstable_cache` so the sitemap is regenerated at most once per
+ * revalidation window. This keeps response times fast for crawlers while
+ * still reflecting recent changes on the site.
+ *
+ * Tagged with `"sitemap"` so the on-demand revalidation webhook can
+ * clear this cache immediately after content changes.
+ *
+ * @see https://nextjs.org/docs/app/api-reference/functions/unstable_cache
  */
-export const revalidate = Number(process.env.SITEMAP_REVALIDATE_SECONDS) || 3600
+const getCachedSitemap = unstable_cache(
+  async () => {
+    const staticEntries = buildStaticEntries()
+    const { gameEntries, deviceEntries } = await fetchDynamicEntries()
+    return [...staticEntries, ...gameEntries, ...deviceEntries]
+  },
+  ["sitemap"],
+  {
+    revalidate: REVALIDATE_SECONDS,
+    tags: ["sitemap"],
+  },
+)
 
 export default async function sitemap(): Promise<MetadataRoute.Sitemap> {
-  const staticEntries = buildStaticEntries()
-  const { gameEntries, deviceEntries } = await fetchDynamicEntries()
-
-  return [...staticEntries, ...gameEntries, ...deviceEntries]
+  return getCachedSitemap()
 }