Update the E2E Tests on Atomic All workflow to run with Playwright

[eduardoumpierre]

Important

This issue depends on #10240. There is a PR open for the issue. Please build this issue's PR on top of PR #10276
Context threads:

• Original thread: p1738179003748179-slack-C01B8KNUYSW
• Follow up thread: p1738248569627589-slack-C01B8KNUYSW

Description

As part of the release process, the E2E Tests on Atomic - All workflow is run on a different test site. We need to update it to run the tests with Playwright.

Acceptance criteria

• The workflow has been updated
• The tests are running on the Atomic site
• The tests are passing (or a new issue was filed to address that)

[eduardoumpierre]

I'm closing this issue since its related PR was already merged.