Adds Playwright E2E and Vitest test infrastructure

Integrates Playwright for end-to-end browser testing with automated web server setup, example smoke tests, and CI-compatible configuration. Introduces Vitest, Testing Library, and related utilities for fast component and unit testing.

Updates scripts, development dependencies, and lockfile to support both test suites. Establishes unified testing commands for local and CI workflows, laying groundwork for comprehensive automated UI and integration coverage.

.gitignore

@@ -36,3 +36,7 @@ yarn-error.log*
 next-env.d.ts
 
 .turbo/
+
+playwright-report/
+
+test-results/