test(04-01): add table control E2E tests

- Test control page displays buttons
- Test home action can be triggered
- Test navigation bar shows all page links

frontend/e2e/table-control.spec.ts

@@ -0,0 +1,47 @@
+import { test, expect } from '@playwright/test'
+import { setupApiMocks, resetMockStatus } from './mocks/api'
+
+test.describe('Table Control E2E', () => {
+  test.beforeEach(async ({ page }) => {
+    resetMockStatus()
+    await setupApiMocks(page)
+
+    // Add route for send_home
+    await page.route('**/send_home', async route => {
+      await route.fulfill({ json: { success: true } })
+    })
+  })
+
+  test('displays control page with buttons', async ({ page }) => {
+    await page.goto('/table-control')
+
+    // Should show control buttons
+    await expect(page.getByRole('button', { name: /home/i })).toBeVisible()
+    await expect(page.getByRole('button', { name: /stop/i })).toBeVisible()
+  })
+
+  test('can trigger home action', async ({ page }) => {
+    await page.goto('/table-control')
+
+    // Find and click home button
+    const homeButton = page.getByRole('button', { name: /home/i })
+    await expect(homeButton).toBeVisible()
+
+    // Click should not throw error
+    await homeButton.click()
+
+    // Button should still be visible (action completed)
+    await expect(homeButton).toBeVisible()
+  })
+
+  test('navigation bar shows all pages', async ({ page }) => {
+    await page.goto('/table-control')
+
+    // All nav items should be visible
+    await expect(page.getByRole('link', { name: /browse/i })).toBeVisible()
+    await expect(page.getByRole('link', { name: /playlists/i })).toBeVisible()
+    await expect(page.getByRole('link', { name: /control/i })).toBeVisible()
+    await expect(page.getByRole('link', { name: /led/i })).toBeVisible()
+    await expect(page.getByRole('link', { name: /settings/i })).toBeVisible()
+  })
+})