REST API

function pm_custom_uri_rest() {
    register_rest_field(
        'product',
        'custom_uri',
        array(
            'get_callback' => 'rest_get_custom_uri',
            'update_callback' => 'rest_update_custom_uri',
            'schema' => array(
                'description' => 'The value of "Current URI" field.',
                'type' => 'string',
                'context' => array('view', 'edit')
            )
        )
    );
}
add_action('rest_api_init', 'pm_custom_uri_rest');

function rest_get_custom_uri($post, $field_name, $request) {
    return (!empty($post['id'])) ? Permalink_Manager_URI_Functions_Post::get_post_uri($post['id']) : '';
}

function rest_update_custom_uri($value, $post, $field_name) {
    // Perform Validation of input
    if (!$value || !is_string($value)) {
        return;
    }

    // Get product ID
    if(!empty($post->ID)) {
        $post_id = $post->ID;
    } elseif(method_exists($post, 'get_id')) {
        $post_id = $post->get_id();
    }

    if(!empty($post_id)) {
        Permalink_Manager_URI_Functions::save_single_uri($post_id, $value, false, true);
    }
}

function pm_rest_custom_uri_after_rest_insert($post, $request, $is_new_post) {
    if($is_new_post && class_exists('Permalink_Manager_URI_Functions_Post')) {
        // 1. Generate the URI
        $new_uri = Permalink_Manager_URI_Functions_Post::get_default_post_uri($post);

        // 2. Save the URI in DB
        Permalink_Manager_URI_Functions::save_single_uri($post->ID, $new_uri, false, true);
    }
}
add_action('rest_after_insert_product', 'pm_rest_custom_uri_after_rest_insert', 9, 3);