Linking to the most recent post in a Custom Post Type

As long as Pods creates standard custom post types, you can simply update the arguments passed to WP_Query . The$post_type parameter will allow you to filter the results based on the specified post type (string) or post types (array).

$latest = new WP_Query( array(
    'category_name' => $request->query_vars['category_name'],
    'posts_per_page' => 1,
    'post_type' => array ( 'post', 'your_custom_post_type' ),
) );