Add first and last CSS class to WordPress navigation menu items by using filters. CSS class will be added automatically without need for tinkering with WordPress admin. Note: Last class will be added to the last menu item. If the last menu item has sub menu, the last class will be added to the last item of that sub menu.

menu-css-class.php

<?php
//Add extra css classes to menu items
function mytheme_nav_menu_css_class( $classes = array(), $item, $args ) {
    $location_name = 'header';

    if($args->theme_location== $location_name){//Limit to this menu location only
        
        if ( ( $locations = get_nav_menu_locations() ) && isset( $locations[ $location_name ] ) ) {
            $main_nav = wp_get_nav_menu_object( $locations[ $location_name ] );

            if ($item->menu_order == 1) {
                $classes[] = 'first'; //First menu item
            }
            if ($item->menu_order >= $main_nav->count) {
                $classes[] = 'last'; //Overall last menu item
            }
        }
    }
    return $classes;
}
add_filter( 'nav_menu_css_class', 'mytheme_nav_menu_css_class', 10, 3 );