Use the protect-status package in the Protect plugin

[elliottprogrammer]

In this PR we are implementing use of the protect-status package that was created in #37894. Additionally, this PR can serve as a method of testing PR #37894.

Proposed changes:

• Remove all occurrences of any protect-status related code.
• Require and use the protect-status package.

Other information:

• Have you written new tests for your changes, if applicable?
• Have you checked the E2E test CI results, and verified that your changes do not break them?
• Have you tested your changes on WordPress.com, if applicable (if so, you'll see a generated comment below with a script to run)?

Jetpack product discussion

This PR is part of the PT: Add value to the active Protect product card on My Jetpack project: pbNhbs-aP6-p2

Does this pull request change what data or activity we track or use?

No

Testing instructions:

• Create a Jurassic Ninja site with the Jetpack Beta Plugin, running Protect branch add/protect-status-pkg-to-plugin.
• Connect Jetpack
• Activate the Protect plugin and verify everything is working fine as expected, and with no errors.

[github-actions]

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Protect plugin:

• Next scheduled release: July 2, 2024.
• Scheduled code freeze: June 24, 2024.

If you have any questions about the release process, please ask in the #jetpack-releases channel on Slack.

[robertsreberski]

The refactor looks solid 💪

[robertsreberski]

I think we could still keep it called Protect_Status_REST_Controller so it will be explicit in the code - what do you think?

[elliottprogrammer]

Yeah I agree, Thanks Robert! 😃

The base branch was changed.

[robertsreberski]

Still looks good after the rebase 👍