Fix public home routing and add home smoke test

tests/e2e/public-smoke.spec.ts

@@ -4,10 +4,12 @@ import { captureEvidence } from './helpers/evidence';
 const baseUrl = (process.env.E2E_BASE_URL ?? 'https://www.taxbaik.com/taxbaik').replace(/\/$/, '');
 
 test.describe('public smoke', () => {
-  test('@smoke loads the main public pages with SEO basics', async ({ page }) => {
+  test('@smoke loads the home page and key public pages with SEO basics', async ({ page }) => {
     await page.goto(baseUrl);
     await expect(page).toHaveTitle(/백원숙 세무회계/);
     await expect(page).not.toHaveTitle(/관리자/);
+    await expect(page.getByRole('heading', { name: /세금과 자산|백원숙 세무회계/ })).toBeVisible();
+    await expect(page.getByRole('link', { name: /상담 신청|무료 상담 신청/ })).toBeVisible();
     await expect(page.locator('meta[name="description"]')).toHaveAttribute('content', /사업자 기장|부동산|종합소득세/);
     await expect(page.getByRole('heading', { name: /상담 과정/ })).toBeVisible();