Fix flaky E2E tests in specs/modules/analytics/setup-with-account-with-tag.test.js.

[techanvil]

Feature Description

We still have a number of E2E tests failing with some regularity in our CI test runs. The task of fixing them has been split into four issues in order to make it easier to investigate and fix. See #10108, #10110, #10111.

setting up the Analytics module with an existing account and existing tag › informs about an existing tag that matches the current selected property

Example: https://github.com/google/site-kit-wp/actions/runs/12880056623/job/35908487009#step:11:249

Details

FAIL specs/modules/analytics/setup-with-account-with-tag.test.js (17.321 s)
  ● setting up the Analytics module with an existing account and existing tag › informs about an existing tag that matches the current selected property

    expect(jest.fn()).not.toHaveErrored(expected)

    Expected mock function not to be called but it was called with:
    ["Google Site Kit API Error method:GET datapoint:container-destinations type:modules identifier:analytics-4 error:\"The response is not a valid JSON response.\""]

      at Object.assertExpectedCalls (../../node_modules/@wordpress/jest-console/build/@wordpress/jest-console/src/index.js:36:4)
          at runMicrotasks (<anonymous>)

setting up the Analytics module with an existing account and existing tag › does allow Analytics to be set up with an existing tag if it is a GA4 tag

Example: https://github.com/google/site-kit-wp/actions/runs/12881028076/job/35910945895#step:11:260

Details

FAIL specs/modules/analytics/setup-with-account-with-tag.test.js (18.277 s)
  ● setting up the Analytics module with an existing account and existing tag › does allow Analytics to be set up with an existing tag if it is a GA4 tag

    TimeoutError: waiting for selector `.googlesitekit-publisher-win--win-success` failed: timeout 5000ms exceeded

      230 | 		} );
      231 | 
    > 232 | 		await page.waitForSelector(
          | 		           ^
      233 | 			'.googlesitekit-publisher-win--win-success'
      234 | 		);
      235 | 		await expect( page ).toMatchElement(

      at new WaitTask (../../node_modules/puppeteer/src/common/DOMWorld.ts:788:28)
      at DOMWorld.waitForSelectorInPage (../../node_modules/puppeteer/src/common/DOMWorld.ts:642:22)
      at Object.internalHandler.waitFor (../../node_modules/puppeteer/src/common/QueryHandler.ts:78:19)
      at DOMWorld.waitForSelector (../../node_modules/puppeteer/src/common/DOMWorld.ts:500:25)
      at Frame.waitForSelector (../../node_modules/puppeteer/src/common/FrameManager.ts:1161:47)
      at Page.waitForSelector (../../node_modules/puppeteer/src/common/Page.ts:3127:29)
      at Object.<anonymous> (specs/modules/analytics/setup-with-account-with-tag.test.js:232:14)
          at runMicrotasks (<anonymous>)

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Acceptance criteria

• The tests listed in the Feature Description should pass every time in CI.

Implementation Brief

Test Coverage

QA Brief

Changelog entry