Build/Test Tools: Migrate Puppeteer tests to Playwright.

As per the migration plan shared last year, this migrates all browser-based tests in WordPress core to use Playwright.
This includes end-to-end, performance, and visual regression tests.

Props swissspidy, mamaduka, kevin940726, bartkalisz, desrosj, adamsilverstein.
Fixes #59517.

git-svn-id: https://develop.svn.wordpress.org/trunk@56926 602fd350-edb4-49c9-b593-d223f7449a82

.github/workflows/coding-standards.yml

@@ -142,8 +142,6 @@ jobs:
       contents: read
     timeout-minutes: 20
     if: ${{ github.repository == 'WordPress/wordpress-develop' || github.event_name == 'pull_request' }}
-    env:
-      PUPPETEER_SKIP_DOWNLOAD: ${{ true }}
 
     steps:
       - name: Checkout repository