feat: Add E2E tests with Playwright

Description

The project currently has excellent test coverage for data validation (4316 tests) but lacks end-to-end (E2E) testing for critical user flows.

Problem

• No E2E tests exist for interactive features like quizzes, games, search
• User journeys are not tested from browser perspective
• Risk of UI regressions going undetected

Proposed Solution

Add Playwright for E2E testing covering:

• Quiz taking flow (/quizzes/[slug])
• Game interactions (multiple game pages)
• Search functionality
• Navigation across pages
• Dark mode toggle
• Mobile responsive behavior

Acceptance Criteria

• Install and configure Playwright
• Add E2E tests for quiz completion flow
• Add E2E tests for at least 2 games
• Add E2E tests for search
• Add E2E tests for navigation
• Configure GitHub Actions workflow for E2E tests
• Add test documentation

Files to Modify

• package.json - Add Playwright dependency
• playwright.config.ts - Create configuration
• e2e/ - New directory for E2E tests
• .github/workflows/e2e.yml - New CI workflow

Start with package.json and the existing application routes, especially /quizzes/[slug], then review the proposed playwright.config.ts and e2e/ layout. Define coverage for quiz completion, two games, search, navigation, dark mode, and mobile behavior, and use .github/workflows/e2e.yml to verify the suite runs in CI. Done means the listed acceptance criteria and test documentation are complete.