Insert Link: consider adding the post type for pages and CPTs or the date for posts in suggested link search results

[designsimply]

Requested in #9660.
Mentioned at #6392 (comment).

Consider adding the post type (e.g. Page, CPT name, or the date for posts) on the right for suggested links similar to how the classic editor does:

^{Example screenshot from #2084 showing how post types are listed in link suggestions in the classic editor.}

[chrisvanpatten]

I would love this - even better if there's a way to build it into the REST API search endpoint as a "Secondary Search Context" label (or something like that) which could be filtered so post types could provide their own helpful string, similar to how the built-in "Post" post-type shows a date instead of the post type name.

[edwinhamers]

+1 for me.. Sorry to open my own issue for it!

#16534 (comment)

[sarahmonster]

There are some mockups that relate to this on #8573.

[mtias]

This has been implemented. For reference: