test(e2e): align auth + public smoke tests with new / and /home routing

Playwright specs still asserted the pre-refactor URLs and failed on CI:
- auth.spec.ts expected post-login to land at `/`; now `/home`.
- public.spec.ts expected unauth redirect to `/landing`; now `/`.
- public.spec.ts's landing-loads test navigated to `/landing` (a stale-
  bookmark redirect); point it directly at `/`.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

frontend/e2e/auth.spec.ts

@@ -7,7 +7,7 @@ test.describe('authentication smoke tests', () => {
   test('team admin can sign in through the login form', async ({ page }) => {
     await signIn(page)
 
-    await expect(page).toHaveURL(/\/$/)
+    await expect(page).toHaveURL(/\/home$/)
     await expect(page.getByTestId('app-shell')).toBeVisible()
   })
 })