Set Taxonomy based on post status

This is what works with the help of WebElaine above. I had to pass the postID to has_category() and then set variables.

function add_categories_automatically($postID) {
    $p_published = get_post_status($postID) == 'publish';
    $p_draft = get_post_status($postID) == 'draft';
    $p_cat = has_category( 'billed', $postID);  
    
    if ($p_draft == 'draft'){
        $catsID = array(1); //active
        wp_set_post_categories($postID, $catsID);
    }
    if ($p_published == 'publish'){
        $catsID = array(5); //complete
        wp_set_post_categories($postID, $catsID);
    }
    if($p_published == 'publish' && $p_cat ){
        $catsID = array(16); //billed
        wp_set_post_categories($postID, $catsID);
    }
}
add_action('save_post', 'add_categories_automatically');