PHP

function.php

<php
    function register_custom_post_type() {
    register_post_type('slug-name', array(
        'label' => 'ブログ',
        'public' => true,
        'show_in_rest' => true, // REST API を有効化
        'supports' => array('title', 'editor', 'thumbnail'),
     ));
   }
  add_action('init', 'register_custom_post_type');
?>
<php
    function add_thumbnail_to_rest_api($data, $post, $context) {
    if (has_post_thumbnail($post->ID)) {
        $data->data['thumbnail'] = get_the_post_thumbnail_url($post->ID, 'full');
    } else {
        $data->data['thumbnail'] = get_template_directory_uri() . '/img-path';
    }
    return $data;
   }
  add_filter('rest_prepare_post', 'add_thumbnail_to_rest_api', 10, 3);
?>