feat(frontend): connect Next.js server components to Go backend REST API with resilient fallback

- Implement typed REST API client in refer_landing_page/lib/api.ts
- Support API_BASE_URL environment variable with graceful fallback to static content
- Connect Home page (projects, areas, stats), Members page (active, alumni), Publications (highlights, list, patents), Lectures, and Standardization pages to backend endpoints
- Pass all 12 SSG build, TypeScript, ESLint, and E2E quality gates

refer_landing_page/app/publications/page.tsx

@@ -1,13 +1,23 @@
 import type { Metadata } from "next";
 import { CategoryNav } from "./_components/CategoryNav";
-import { publications } from "../../content/publications";
+import { publications as staticPubs, patents as staticPatents } from "../../content/publications";
+import { getPublications, getPatents } from "../../lib/api";
 
 export const metadata: Metadata = {
   title: "Publications",
   description: "AI Agent Networking Lab (ANL) research publications and patents overview",
 };
 
-export default function PublicationsIndexPage() {
+export default async function PublicationsIndexPage() {
+  const publications = (await getPublications()) ?? staticPubs;
+  const patents = (await getPatents()) ?? staticPatents;
+
+  const counts = {
+    "intl-journal-conf": publications.filter((p) => p.category === "intl-journal-conf").length,
+    "domestic-journal-conf": publications.filter((p) => p.category === "domestic-journal-conf").length,
+    patent: patents.length,
+  };
+
   // Selected representative publications (curated via database isHighlight flag)
   const highlights = publications.filter((p) => p.isHighlight);
 
@@ -22,7 +32,7 @@ export default function PublicationsIndexPage() {
 
       {/* Category Summary Cards */}
       <section className="pt-6 md:pt-8 border-t border-line">
-        <CategoryNav />
+        <CategoryNav counts={counts} />
       </section>
 
       {/* Highlights Section */}