Add this snippet into functions.php and if you want to implement it in any custom post type then just change the filter hook name: rest_prepare_{custom_post_type}
function dandd_post_json_fields( $data, $post, $context ) {
$image_attributes = wp_get_attachment_image_src( $data->data['featured_media'] );
$post_categories = wp_get_post_categories( $data->data['id'] );
$cats = array();
foreach($post_categories as $c){
$cat = get_category( $c );
$cats[] = array( 'name' => $cat->name );
}
return [
'id' => $data->data['id'],
'date' => $data->data['date'],
'link' => $data->data['link'],
'title' => $data->data['title']['rendered'],
'excerpt' => $data->data['excerpt']['rendered'],
'content' => $data->data['content']['rendered'],
'image' => $image_attributes[0],
'categories' => $cats,
];
}
add_filter( 'rest_prepare_post', 'dandd_post_json_fields', 12, 3 );