Feature Description

In #5695, we introduced async status checks for Site Kit tags on the Site Health "Status" tab which primarily surfaces recommendations and errors to users. This will help surface issues if tags are not being placed or if they're not detected.

It would also be useful to additionally include this information in the "Info" tab of Site Heath, which SK has long extended with its own section. This was originally planned for 5695 but was removed from the scope due to complications with the async nature of the checks. This can be revisited however, as core itself does at least one async check for the site health info: directory sizes. The complication comes from needing to update both the HTML in the table on the page, but also the plain text version of that data which can be copied to the clipboard which is separately stored in an HTML attribute on the button. See https://github.com/WordPress/WordPress/blob/e19c18cba94edea039c8b137138ba94df0097d06/wp-admin/js/site-health.js#L375-L438

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Implementation Brief

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