terms - How to order and count get_terms by specific post type?|Programmer puzzle solving

I want to get a list of taxonomy "company" terms which have a particular meta value and which are associated with posts of custom type "viewpoint".

Beginning with getting Viewpoint posts, as per recent answer, WordPress' get_posts() supports populating the resulting array with a fields value of only post ids...

$vp_post_args = array(
  'post_type' => $post_type,
  'fields' => 'ids',
  'nopaging'  => 'true',
);
$viewpoint_posts = get_posts($vp_post_args);

Thus, $viewpoint_posts contains only a list of 'viewpoint' post IDs. This list can then be used to feed a get_terms() call that is further constrained by 'taxonomy' => 'company' and a related 'meta_query'...

// 2a. Get Companies matching Tag
$vp_org_term_args_for_shortlist = array(
    // Load Viewpoint post IDs in to get_terms():
    'object_ids' => $viewpoint_posts,
    // Only get Company terms
    'taxonomy'   => 'company',
    // Only company terms with Tags Checkbox value:
    'meta_query' => array(
         array(
            'key'       => 'tags',
            'value'     => $tag_section,
            'compare'   => 'LIKE'
         )
    ),
    // Order
    'orderby'    => 'count',
    'order'      => 'desc',
    'hide_empty' => false,
    // Number of companies to show in list
    'number'     => 11,
);
$viewpoint_org_terms_for_shortlist = get_terms($vp_org_term_args_for_shortlist);

So far, so good. This all works.

My problem is around the get_terms parameter 'orderby' => 'count'. You see, count above denotes a term's total post count of any post type. In my case, my 'company' taxonomy is in use by more than one post type, but here I only want to be dealing with posts of type 'viewpoint'.

How do I get get_terms() to only think within the context of a particular post type? After all, I have already taken the step of feeding it IDs of posts which all had the same post type.

Here is my current output part...

// List organisations:
echo '<div class="list-group list-unstyled">';
foreach ($viewpoint_org_terms_for_shortlist as $org_short_single) {
     echo '<a href="' . esc_url( get_term_link( $org_short_single ) ) . '" alt="' . esc_attr( sprintf( __( 'View all post filed under %s', 'my_localization_domain' ), $org_short_single->name ) ) . '" class="list-group-item list-group-item-action d-flex justify-content-between align-items-center">';
     echo '<span><img src="='.get_field( 'domain', $org_short_single ).'" class="mr-2">' . $org_short_single->name . '</span>';
     echo '<span class="badge badge-primary badge-pill">'.$org_short_single->count.'</span>';
     echo '</a>';
}
echo '</div>';

But I want to both:

order my company terms list by associated number of viewpoint posts (not by posts of all types).
output a post count for said company term that is post type viewpoint-specific (not $org_short_single->count, which again encompasses all posts)

Programmer puzzle solving

terms - How to order and count get_terms by specific post type?

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