Fix invitation flow error by adding SessionProvider

- Add SessionProvider to root Providers for NextAuth React hooks
- Add error handling to auth layout to prevent crashes on auth check failure
- Add MENTOR role redirect in auth layout

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/app/(auth)/layout.tsx

@@ -7,7 +7,13 @@ export default async function AuthLayout({
 }: {
   children: React.ReactNode
 }) {
-  const session = await auth()
+  let session = null
+  try {
+    session = await auth()
+  } catch (error) {
+    // Auth check failed, continue as unauthenticated
+    console.error('Auth check failed in auth layout:', error)
+  }
 
   // Redirect logged-in users to their dashboard
   if (session?.user) {
@@ -18,6 +24,8 @@ export default async function AuthLayout({
       redirect('/jury')
     } else if (role === 'OBSERVER') {
       redirect('/observer')
+    } else if (role === 'MENTOR') {
+      redirect('/mentor')
     }
   }