nikoshot,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
.new{
background-color: #008000;
}
</style>
<script>
addEventListener("click", event => {
const variant = event.target.closest(".class_variant")
if(!variant) return;
const parent = variant.closest(".product-cut__main-info");
const btn = parent.querySelector(".buy__btn");
btn.classList.add("new");
});
</script>
</head>
<body>
<div class="product-cut__main-info">
<div class="class_name"></div>
<div class="class_foto"></div>
<div class="class_variant">variant</div>
<div class="class_price"></div>
<div class="class_info">
<button class="buy__btn">btn</button>
</div>
</div>
</body>
</html>