Filters the output of the featured image for a custom post type, based on a taxonomy with a custom image field.

filter_featured_img_by_taxonomy.php

<?php

/**
 * 
 * Filter the thumbnail for Providers based on taxonomy
 * @param mixed $thumbnail_id
 * @param mixed $post
 * @return mixed
 */
function PREFIX_filter_provider_thumbnail($thumbnail_id, $post)
{

	$post_id = $post->ID;
	$post_type = 'provider';
	$taxonomy = 'specialty';
	$taxonomy_thumb_meta = 'specialty_icon';
	$default_id = 15164; // ID of the default thumbnail (attachment ID)

	// exit early if on backend, or not the correct post type, or thumbnail is already set
	if (is_admin() || $thumbnail_id || get_post_type($post_id) !== $post_type)
		return $thumbnail_id;

	// get terms for the current post: returns array of WP_Term Objects
	$terms_list = get_the_terms($post_id, $taxonomy);

	// check if there are any terms, and if not return the default
	if (!$terms_list || !is_array($terms_list))
		return $default_id;

	// filter the $terms_list to only include top-level tems (i.e. "parent" = 0)
	$terms_list = array_filter($terms_list, function ($term) {
		return (int) $term->parent === 0;
	});

	// get the first term
	$terms_list = array_values($terms_list);
	$first_term = array_shift($terms_list);

	// get the attachment_id for the first term
	$term_thumbnail_id = get_term_meta($first_term->term_id, $taxonomy_thumb_meta, true);

	// set the thumbnail
	$thumbnail_id = ($term_thumbnail_id) ? $term_thumbnail_id : $default_id;

	// output
	return (int) $thumbnail_id;
}
add_filter('post_thumbnail_id', 'PREFIX_filter_provider_thumbnail', 10, 2);



// Register the column
function PREFIX_add_taxonomy_column_hooks()
{
	$taxonomy = 'specialty';

	add_filter('manage_' . $taxonomy . '_custom_column', 'PREFIX_specialty_rows', 15, 3);
	add_filter('manage_edit-' . $taxonomy . '_columns', 'PREFIX_specialty_columns');
}
add_action('admin_init', 'PREFIX_add_taxonomy_column_hooks');

function PREFIX_specialty_rows($row, $column_name, $term_id)
{
	//get thumb
	$thumb_id = get_term_meta($term_id, 'specialty_icon', true);
	$thumb_img = ($thumb_id) ? wp_get_attachment_image($thumb_id, [60,60]) : '';

	if ('thumb' === $column_name) {
		echo $thumb_img;
	}
}
function PREFIX_specialty_columns($original_columns)
{
	$new_columns = $original_columns;
	array_splice($new_columns, 1);
	$new_columns['thumb'] = esc_html__('Thumb', 'taxonomy-images');
	return array_merge($new_columns, $original_columns);
}

This is currently using an example post_type of "provider" with a taxonomy called "specialty." This Taxonomy has the custom field "specialty_icon" which returns the attachment ID. If no featured image is found for the current post, it tries to replace it with the image set for the top-level term in that taxonomy. Can also set a default (attachment ID) if no image is set as featured, or if there is no image in the post terms.