How can I create a new WordPress menu programmatically and assign the menu item to the new menu
You can use WordPress native function wp_create_nav_menu to create a new menu and using wp_update_nav_menu_item to assign the menu items
$menuname = "New Menu";
$menu_exists = wp_get_nav_menu_object( $menuname );
if( !$menu_exists){
$menu_id = wp_create_nav_menu($menuname);
wp_update_nav_menu_item($menu_id, 0, array(
'menu-item-title' => __('Home'),
'menu-item-classes' => 'home',
'menu-item-url' => home_url( '/' ),
'menu-item-status' => 'publish'));
}