Add options to the “Screen Options” section on the “Menus” editor

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Figured this out by looking through the WordPress source code 🙂

function new_site_add_custom_screen_options($args) {
    $args["custom_option_1"] = __("Custom Option 1", "new_site");
    $args["custom_option_2"] = __("Custom Option 2", "new_site");

    return $args;
}
add_filter("manage_nav-menus_columns", "new_site_add_custom_screen_options", 20);