feat: implement API client with JSON handling and error mapping; enhance routing and state management in app shell

flutter/lib/core/api/api_exception.dart

@@ -0,0 +1,25 @@
+enum ApiErrorType {
+  unauthorized,
+  forbidden,
+  server,
+  network,
+  unknown,
+}
+
+class ApiException implements Exception {
+  final ApiErrorType type;
+  final int? statusCode;
+  final String message;
+
+  const ApiException({
+    required this.type,
+    required this.message,
+    this.statusCode,
+  });
+
+  @override
+  String toString() {
+    final status = statusCode == null ? '' : ' (HTTP $statusCode)';
+    return 'ApiException$type$status: $message';
+  }
+}