implement auth error page and moved auth-related pages to /auth path

src/app/page.tsx

@@ -143,13 +143,13 @@ export default function HomePage() {
         headers: { 'Content-Type': 'application/json' },
         body: JSON.stringify({ prompt: aiPrompt })
       })
-      
+
       if (res.status === 401) {
         alert('Please sign in to use AI features.')
         setAiLoading(false)
         return
       }
-      
+
       const data = await res.json()
 
       if (Array.isArray(data) && data.length > 0) {
@@ -254,7 +254,7 @@ export default function HomePage() {
             Sign in to unlock AI-powered calendar features
           </div>
           <Button variant="outline" size="sm" asChild>
-            <a href="/signin">Sign In</a>
+            <a href="/auth/signin">Sign In</a>
           </Button>
         </div>
       )}