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Update:

While I've been researching this issue I've found an issue with the terminology I'm using:

I don't just want search results to encompass custom meta, I also need them to encompass custom taxonomies (I've just learnt that these things are not the same).

So for a cpt of type 'book' with a custom taxonomy of type 'genre', I'd like a search that is limited to the cpt and that has the search string 'horror' return all results that have 'horror' attached as a value to the custom taxonomy 'genre'.

I figured it out.

In the function to display fields from the related CPT's, I should have used the correct id: the id of the relationship that I initially created.

So the corrected function reads like this:

$connected = new WP_Query( array(
‘relationship’ => array(
‘id’ => ‘connect_conversations_to_people’,
‘from’ => get_the_ID(), // You can pass object ID or full object
),
‘nopaging’ => true,
) );
while ( $connected->have_posts() ) : $connected->the_post();
?>
“><?php the_title(); ?>
<?php
endwhile;
wp_reset_postdata();