Restores setting the site's logo, icon, and wp-admin's back button image (which defaults to W).
Prior to [56566], the site logo and icon were unconditionally added to the index. [56566] changed this by conditionally adding them if either the `_links` or `_embedded` fields were included. However, these fields are not included when using the Site Logo block, as it uses the `site_logo`, `site_icon`, and `site_icon_url` fields instead.
This changeset restores the functionality by checking specifically for the `site_*` fields when neither of the `_links` or `_embedded` fields are present.
Follow up to [56566].
Reviewed by jorbin.
Merges [57147] to the 6.4 branch.
Props antonvlasenko, hellofromTonya, ironprogrammer, priethor, wildworks.
Fixes#59935.
Built from https://develop.svn.wordpress.org/branches/6.4@57154
git-svn-id: http://core.svn.wordpress.org/branches/6.4@56665 1a063a9b-81f0-0310-95a4-ce76da25c4cd
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