Fix flaky E2E tests

[aaemnnosttv]

Summary

Addresses issue:

• Fix flaky E2E tests #8229

Relevant technical choices

PR Author Checklist

• My code is tested and passes existing unit tests.
• My code has an appropriate set of unit tests which all pass.
• My code is backward-compatible with WordPress 5.2 and PHP 7.4.
• My code follows the WordPress coding standards.
• My code has proper inline documentation.
• I have added a QA Brief on the issue linked above.
• I have signed the Contributor License Agreement (see https://cla.developers.google.com/).

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Code Reviewer Checklist

• Run the code.
• Ensure the acceptance criteria are satisfied.
• Reassess the implementation with the IB.
• Ensure no unrelated changes are included.
• Ensure CI checks pass.
• Check Storybook where applicable.
• Ensure there is a QA Brief.
• Ensure there are no unexpected significant changes to file sizes.

Merge Reviewer Checklist

• Ensure the PR has the correct target branch.
• Double-check that the PR is okay to be merged.
• Ensure the corresponding issue has a ZenHub release assigned.
• Add a changelog message to the issue.

[techanvil]

Great work here @aaemnnosttv!

I see the E2E suite has passed twice in a row with no failures for this PR, which is a very pleasing sight to behold, as it seems to have been failing every single time recently up until now.

I've left a handful of minor comments.

One additional point, although not technically in scope, it would be nice to clear out the last remaining reference to accounts-properties-profiles:

site-kit-wp/tests/phpunit/integration/Core/Modules/REST_Modules_ControllerTest.php

Line 735 in 22dab9e

$request = new WP_REST_Request( 'POST', '/' . REST_Routes::REST_ROOT . '/modules/non-existent-module/data/accounts-properties-profiles' );

[techanvil]

LGTM, nice one @aaemnnosttv!