Append a parametter at first or last to a certain URL

I got my code working now. Here is the below code that append that extra parameter to the end of the URL specified above.

    add_action('init', 'add_custom_query_for_search');
function add_custom_query_for_search(){
    global $wp;
    
    $tempUrl = home_url() . add_query_arg( $wp->query_vars ) . '&propertyType=RNT';
    
    if( ! isset($_GET['propertyType']) && (strpos($tempUrl, 'homes-for-sale-search') !== false) ){
        wp_redirect($tempUrl);
        die;
    }
}