fix login

lib/screens/splash_screen.dart

@@ -1,12 +1,12 @@
-/// First route shown after launch. Hands off to [MainShell] after a short delay.
+/// First route shown after launch. Hands off to [AuthGate] after a short delay.
 library;
 
 import 'package:flutter/material.dart';
 
 import '../utils/constants.dart';
-import 'main_shell.dart';
+import 'auth_gate.dart';
 
-/// Branded splash with a fade-in logo. Replaced by the bottom-nav shell.
+/// Branded splash with a fade-in logo. Replaced by the auth gate.
 class SplashScreen extends StatefulWidget {
   const SplashScreen({super.key});
 
@@ -32,17 +32,17 @@ class _SplashScreenState extends State<SplashScreen>
       CurvedAnimation(parent: _controller, curve: Curves.easeOutBack),
     );
     _controller.forward();
-    _goToShell();
+    _goToAuthGate();
   }
 
-  Future<void> _goToShell() async {
+  Future<void> _goToAuthGate() async {
     await Future<void>.delayed(kSplashDuration);
     if (!mounted) return;
     Navigator.of(context).pushReplacement(
       PageRouteBuilder<void>(
         pageBuilder: (_, animation, _) => FadeTransition(
           opacity: animation,
-          child: const MainShell(),
+          child: const AuthGate(),
         ),
         transitionDuration: const Duration(milliseconds: 400),
       ),