fix(web): validate question input before divination and fix logout flow

- Add validation for question text in ManualDivinationPage and AutoDivinationPage
- Fix logout flow to call backend API before clearing local auth
- Show error message when question is empty before starting interpretation

web/src/components/SettingsPage.tsx

@@ -21,11 +21,14 @@ export default function SettingsPage({ locale, settings: s }: Props) {
     if (!confirm(s.logoutConfirm)) return;
 
     setLogoutLoading(true);
-    // Clear local auth immediately and redirect
+    try {
+      // Call backend logout first (needs auth)
+      await logout();
+    } catch {
+      // Ignore logout API errors
+    }
+    // Clear local auth and redirect
     clearAuth();
-    // Fire backend logout in background (don't wait)
-    logout().catch(() => {});
-    // Redirect to login
     redirectToLogin();
   };