Introduce Playwright functional tests

[bmuenzenmeyer]

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The ease (not blaming anyone) at which i18n broke and was fixed via #7394 made me wonder if we could assert website functionality via a functional test suite, such as Playwright. We already have vercel previews.

Maybe we could investigate https://vercel.com/guides/how-can-i-run-end-to-end-tests-after-my-vercel-preview-deployment