Remove final use of internal Site_Kit code.

[thijsoo]

Context

• We no longer rely on internal site kit classes to do our data fetching.

Summary

This PR can be summarized in the following changelog entry:

• Removes unused constructor code.

Relevant technical choices:

Test instructions

Test instructions for the acceptance test before the PR gets merged

This PR can be acceptance tested by following these steps:

• Some smokes tests of the widgets. The code was already not used anymore.

Relevant test scenarios

• Changes should be tested with the browser console open
• Changes should be tested on different posts/pages/taxonomies/custom post types/custom taxonomies
• Changes should be tested on different editors (Default Block/Gutenberg/Classic/Elementor/other)
• Changes should be tested on different browsers
• Changes should be tested on multisite

Test instructions for QA when the code is in the RC

• QA should use the same steps as above.

QA can test this PR by following these steps:

Impact check

This PR affects the following parts of the plugin, which may require extra testing:

UI changes

• This PR changes the UI in the plugin. I have added the 'UI change' label to this PR.

Other environments

• This PR also affects Shopify. I have added a changelog entry starting with [shopify-seo], added test instructions for Shopify and attached the Shopify label to this PR.

Documentation

• I have written documentation for this change. For example, comments in the Relevant technical choices, comments in the code, documentation on Confluence / shared Google Drive / Yoast developer portal, or other.

Quality assurance

• I have tested this code to the best of my abilities.
• During testing, I had activated all plugins that Yoast SEO provides integrations for.
• I have added unit tests to verify the code works as intended.
• If any part of the code is behind a feature flag, my test instructions also cover cases where the feature flag is switched off.
• I have written this PR in accordance with my team's definition of done.
• I have checked that the base branch is correctly set.

Innovation

• No innovation project is applicable for this PR.
• This PR falls under an innovation project. I have attached the innovation label.
• I have added my hours to the WBSO document.

Fixes #

[coveralls]

Pull Request Test Coverage Report for Build 449aed6a5efb35ac4e7445bf1ba68b5ac30c74c7

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.003%) to 52.434%

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Totals
Change from base Build ac5953bc6d67cff34a1889152c3bb4df0547a516:	0.003%
Covered Lines:	29060
Relevant Lines:	56471

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💛 - Coveralls

[pls78]

CR && Acc: ✅