Improve detection of Site Kit being active

[leonidasmi]

Context

Summary

This PR can be summarized in the following changelog entry:

• Fixes a bug for users who have the Site Kit integration enabled, where a fatal error would be thrown for edge cases, like when custom code intervened with the default WP login flow.

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:

• Smoke test the Site Kit integration
  • If you have a site where you already have a Yoast+Site Kit integration, install this PR and confirm that the data shown in the widgets are the same with before
  • In a fresh site, install this PR and go through the Site Kit onboarding to enable the integration without issues
  • Once you have set up the Site Kit integration, confirm that you can see the widgets properly (also with a SEO manager)
  • Deactivate the Site Kit plugin and go to the Yoast dashboard. Confirm that you see again the onboarding widget, at the right position
  • Re-activate Site Kit, make sure you also have Google Analytics connected and confirm that you see the Organic sessions widget in the Yoast dashboard too.

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.

Impact check

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

• Test instructions are impact check

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

• [ x 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 #

[thijsoo]

One tiny comment.