test(web): add Vitest tests for search, auth, public, and admin layouts

- SearchLayout: verifies children pass-through (3 tests)
- AuthLayout: verifies role=main, #main-content, max-w-md centering (5 tests)
- PublicLayout: verifies navbar, ticker strip, footer, compare bar, #main-content (8 tests)
- AdminLayout: verifies sidebar nav, auth guard, loading state, logout, mobile toggle (10 tests)

All 156 web test files pass (1157 total web tests). Pre-existing API test
failures in unrelated modules (auth OTP handler, projects, search indexer,
admin settings encryption) are outside scope of this task.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/web/app/[locale]/(auth)/__tests__/layout.spec.tsx

@@ -0,0 +1,61 @@
+/* eslint-disable import-x/order */
+/**
+ * Kiểm thử AuthLayout: wrapper căn giữa cho trang đăng nhập / đăng ký.
+ */
+import { render, screen } from '@testing-library/react';
+import * as React from 'react';
+import { describe, expect, it } from 'vitest';
+
+import AuthLayout from '../layout';
+
+describe('AuthLayout', () => {
+  it('renders children', () => {
+    render(
+      <AuthLayout>
+        <div data-testid="form">Form đăng nhập</div>
+      </AuthLayout>,
+    );
+    expect(screen.getByTestId('form')).toBeInTheDocument();
+    expect(screen.getByText('Form đăng nhập')).toBeInTheDocument();
+  });
+
+  it('has role="main" on the outer element', () => {
+    render(
+      <AuthLayout>
+        <div>Nội dung</div>
+      </AuthLayout>,
+    );
+    expect(screen.getByRole('main')).toBeInTheDocument();
+  });
+
+  it('has id="main-content" for skip-nav accessibility', () => {
+    const { container } = render(
+      <AuthLayout>
+        <div>Nội dung</div>
+      </AuthLayout>,
+    );
+    expect(container.querySelector('#main-content')).toBeInTheDocument();
+  });
+
+  it('centres the form inside a max-width container', () => {
+    const { container } = render(
+      <AuthLayout>
+        <div>Form</div>
+      </AuthLayout>,
+    );
+    // Inner div has w-full max-w-md
+    const inner = container.querySelector('.max-w-md');
+    expect(inner).toBeInTheDocument();
+  });
+
+  it('renders multiple children', () => {
+    render(
+      <AuthLayout>
+        <h1 data-testid="heading">Tiêu đề</h1>
+        <p data-testid="body">Nội dung</p>
+      </AuthLayout>,
+    );
+    expect(screen.getByTestId('heading')).toBeInTheDocument();
+    expect(screen.getByTestId('body')).toBeInTheDocument();
+  });
+});