Use WordPress Playwright E2E test utils package

Summary

WordPress develops a set of utilities to interact with a WordPress instance using Playwright.

Cf. https://www.npmjs.com/package/@wordpress/e2e-test-utils-playwright

We should try to use this package as a way to facilitate our tests development and maintenance.
So far, it seems not usable because of this bug https://github.com/WordPress/gutenberg/issues/50741

Requirements

• explore an integration of this package with one of our tests
• check if we can use some parts of the package despite the blocking bug

Resources

• https://www.npmjs.com/package/@wordpress/e2e-test-utils-playwright
• https://github.com/WordPress/gutenberg/tree/HEAD/packages/e2e-test-utils-playwright/README.md
• https://github.com/WordPress/gutenberg/issues/38851