WEB-1218: [CI/CD] Remove the duplicated E2E readiness gates from playwright.yml - #3968

Node.js 20 is deprecated. The following actions target Node.js 20 but are being forced to run on Node.js 24: actions/create-github-app-token@v2, actions/github-script@v7. For more information see: https://github.blog/changelog/2025-09-19-deprecation-of-node-20-on-github-actions-runners/