feat: migrate from Cypress to Playwright for E2E testing

- Remove Cypress dependencies and configuration files
- Install @playwright/test with browser support
- Add playwright.config.ts with optimized settings for Next.js
- Migrate existing Cypress tests to Playwright format
- Add new E2E test scripts to package.json
- Configure GitHub Actions workflow for automated testing
- Update .gitignore for Playwright artifacts

BREAKING CHANGE: E2E testing framework changed from Cypress to Playwright

.gitignore

@@ -9,6 +9,12 @@
 # testing
 /coverage
 
+# playwright
+/test-results/
+/playwright-report/
+/blob-report/
+/playwright/.cache/
+
 # next.js
 /.next/
 /out/