Fix flaky E2E test in specs/modules/analytics/setup-proxy-no-account-no-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, #10109, #10111.

setting up the Analytics module with no existing account and no existing tag via proxy › preserves user-filled values provided and auto-submits after approving permissions

Example: https://github.com/google/site-kit-wp/actions/runs/12876427603/job/35899408029#step:11:245

Details

FAIL specs/modules/analytics/setup-proxy-no-account-no-tag.test.js (18.381 s)
  ● setting up the Analytics module with no existing account and no existing tag via proxy › preserves user-filled values provided and auto-submits after approving permissions

    TimeoutError: Timeout exceeded while waiting for event

      at Timeout.<anonymous> (../../node_modules/puppeteer/src/common/helper.ts:149:9)

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Acceptance criteria

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

Implementation Brief

Test Coverage

QA Brief

Changelog entry