Improve the test coverage for the `fpm-server-requirement-status` endpoint.

## Feature Description

The initial implementation of the test coverage for the `fpm-server-requirement-status` (see https://github.com/google/site-kit-wp/issues/9632) involved mocking the `is_endpoint_healthy()` protected method of the `REST_First_Party_Mode_Controller`, due to difficulty testing the code contained within the method.

Notably, although it's possible to mock `file_get_contents()`, it doesn't appear possible to mock the `$http_response_header` that gets set locally in the `file_get_contents()` caller's scope with off the shelf tooling.

https://github.com/google/site-kit-wp/blob/54f900c534c135682d44e4dfa8834e3891d91ff2/tests/phpunit/integration/Core/Tags/First_Party_Mode/REST_First_Party_Mode_ControllerTest.php#L235-L241

We should improve the test coverage to ensure the code contained in `is_endpoint_healthy()` is covered. Possible angles include:

- Refactoring `REST_First_Party_Mode_Controller` so we pass in say a Guzzle client instance, or our own wrapper to `file_get_contents()`, and use that rather than calling `file_get_contents()` directly, allowing us to pass in a mock client during testing and avoid mocking `is_endpoint_healthy()`.
- Adding E2E test coverage for the endpoint. This comes with its own challenges, notably mocking the health check to `https://g-1234.fps.goog/mpath/healthy` to avoid calling the real Google service from our E2E tests. It looks possible, but would involve some structural changes to our E2E test environment; this was explored during the implementation of 9632, see https://github.com/google/site-kit-wp/pull/9707. A more practical approach requiring less structural changes would be to provide filters for the health check URLs so we could override them during testing. However, the `REST_First_Party_Mode_Controller` described above is probably the best way to proceed here.

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## Acceptance criteria

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## Implementation Brief

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### Test Coverage

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## QA Brief

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## Changelog entry

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Start with tests/phpunit/integration/Core/Tags/First_Party_Mode/REST_First_Party_Mode_ControllerTest.php around lines 235-241 and inspect REST_First_Party_Mode_Controller::is_endpoint_healthy(). Compare the wrapper/client and E2E approaches described in the issue; done means the method's health-check paths are covered without mocking the protected method and the endpoint tests avoid calling the real Google service.

Written by the indexing model from the issue text.