[Website] Fix flaky phpMyAdmin test

[JanJakes]

Motivation for the change, related issues

The phpMyAdmin E2E test seems to be flaky in Firefox:

  ✘  32 [firefox] › packages/playground/website/playwright/e2e/website-ui.spec.ts:433:6 › Database panel › should load and open phpMyAdmin (retry #3) (42.0s)


  1) [firefox] › packages/playground/website/playwright/e2e/website-ui.spec.ts:433:6 › Database panel › should load and open phpMyAdmin 

    Error: expect(locator).toBeVisible() failed

    Locator:  locator('form#insertForm, form[name="insertForm"]')
    Expected: visible
    Received: <element(s) not found>
    Timeout:  10000ms

    Call log:
      - Expect "toBeVisible" with timeout 10000ms
      - waiting for locator('form#insertForm, form[name="insertForm"]')


      472 | 			'form#insertForm, form[name="insertForm"]'
      473 | 		);
    > 474 | 		await expect(pmaForm).toBeVisible({ timeout: 10000 });
          | 		                      ^
      475 | 		await expect(pmaForm).toContainText('Welcome to WordPress.');
      476 |
      477 | 		// Update the post content
        at /home/runner/work/wordpress-playground/wordpress-playground/packages/playground/website/playwright/e2e/website-ui.spec.ts:474:25

    Error Context: packages/playground/website/test-results/website-ui-Database-panel-should-load-and-open-phpMyAdmin-firefox/error-context.md

Implementation details

The issue appears to be that phpMyAdmin handles screen navigation using custom AJAX handlers, which may ignore link clicks when another AJAX request is still in progress. This is implemented in their AJAX module that is exposed globally on window.AJAX.

I tried other approaches like waiting for a loader to disappear, but no luck. This approach seems to be the only reliable one.

Testing Instructions (or ideally a Blueprint)

See the CI passing.