JS based raw menu for Smarty Templates - https://github.com/deshabhishek007/wp-menu-extractor

extracted-menu.tpl

<div id="menu_container"></div>

{literal}
	<script>
		var json_path = "https://DOMAIN.HERE/wp-json/wp-menu-extractor/v2/menus/IDHERE";
		var json_menu, menu_items, menu_markup;
		fetch(json_path)
		.then(json_menu => json_menu.json())
		.then(json_menu =>{
			menu_items = json_menu.items;
			menu_markup = menu(menu_items);
			var menu_el = document.getElementById('menu_container');
			menu_el.innerHTML = menu_markup;
		})
	
		function menu(menu_items){
			var markup = "";
			markup +='<ul>';
			menu_items.forEach(function(item){
			markup += '<li><a href="'+item.url+'" class="'+item.classes+'" target="'+item.target+'">'+item.title+'</a>';
				if (item.children) {
					markup += menu(item.children);
				}
			  markup += '</li>';
			});
			markup +='</ul>';
			return markup;
		}
	</script>
{/literal}