Scripts: Deprecated or remove Puppeteer as e2e test handler

Extracted from #59311.

Now that core is [fully migrated to Playwright](https://github.com/WordPress/gutenberg/issues/38851) and is the recommended library for running e2e tests, let's consider gracefully deprecating or fully removing Puppeteer from the scripts package.