feat: Add automated testing with Vitest and Playwright

- Install Vitest (integration tests for API routes) and Playwright (E2E tests)
- Add vitest.config.ts, playwright.config.ts, src/test/setup.ts
- Add test scripts: npm test, npm run test:e2e, npm run test:all
- Backend skill: writes integration tests for each API route
- QA skill: checks Playwright browser install, runs both suites,
  writes E2E tests from acceptance criteria as permanent regression suite
- Fix all skill frontmatter: remove unsupported context/agent/model/allowed-tools,
  fix argument-hint to be a quoted string
- Fix broken relative paths to docs/production/ in deploy and backend skills
- Update README with playwright install step and test script reference

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

playwright.config.ts

@@ -0,0 +1,22 @@
+import { defineConfig, devices } from '@playwright/test'
+
+export default defineConfig({
+  testDir: './tests',
+  fullyParallel: true,
+  forbidOnly: !!process.env.CI,
+  retries: process.env.CI ? 2 : 0,
+  reporter: 'html',
+  use: {
+    baseURL: 'http://localhost:3000',
+    trace: 'on-first-retry',
+  },
+  projects: [
+    { name: 'chromium', use: { ...devices['Desktop Chrome'] } },
+    { name: 'Mobile Safari', use: { ...devices['iPhone 13'] } },
+  ],
+  webServer: {
+    command: 'npm run dev',
+    url: 'http://localhost:3000',
+    reuseExistingServer: !process.env.CI,
+  },
+})