nmc-15 update auth-intl example to use rules

Author: vordgi

examples/auth-intl/src/app/dk/page.tsx

@@ -1,7 +1,7 @@
 export default function Home() {
     return (
         <div>
-            <p>Home page</p>
+            <p>Home page (dk)</p>
         </div>
     );
 }

examples/auth-intl/src/app/en/page.tsx

@@ -1,7 +1,7 @@
 export default function Home() {
     return (
         <div>
-            <p>Home page</p>
+            <p>Home page (en)</p>
         </div>
     );
 }

examples/auth-intl/src/app/private/page.tsx

@@ -0,0 +1,7 @@
+export default function Private() {
+    return (
+        <div>
+            <p>Private page</p>
+        </div>
+    );
+}

examples/auth-intl/src/middleware.ts

@@ -8,11 +8,11 @@ const intlMiddleware = createMiddleware({
 });
 
 export default chain([
-    intlMiddleware,
+    [intlMiddleware, { exclude: /^\/private(\/.*)?$/ }],
     (req) => {
         if (req.summary.type === "redirect") return FinalNextResponse.next();
     },
-    nextAuth,
+    [nextAuth, { include: /^\/private(\/.*)?$/ }],
 ]);
 
 export const config = {