Rework integration of remote features

[aaemnnosttv]

Summary

Addresses issue:

• Rework integration of remote features for consistency between testing and live applications #8341

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 5.6.
• 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.

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.

[github-actions]

Build files for 26fd284 have been deleted.

[tofumatt]

Looks good, and seems to work fine for me 👍🏻

Just one file header copypasta issue, I'll fix it then merge 👍🏻