// Add an out of stock overlay to product images when all variations are unavailable
//상품 재고가 떨어지면 상품 이미지에 Out of Stock 오버레이 추가

add_action( 'woocommerce_before_shop_loop_item_title', function() {
global $product;
if ( !$product->is_in_stock() ) {
echo '<span class="sold-out-overlay">Sold Out</span>';
}
});

출처: https://launchwoo.com.au/add-a-sold-out-badge-to-out-of-stock-woocommerce-products/

.sold-out-overlay {
background: #654ea3; /* 배경색 - 적절히 수정 */
color: #fff; /* 텍스트 색상 - 적절히 수정 */
font-size: 14px;
font-weight: 600;
padding: 5px 10px;
position: absolute;
right: 50px;
top: 10px;
}