To change Add to cart button on Sold Out products to a custom button image, you can use this code to Website > Website Tools > Custom CSS.
/* sold out add to cart */
.sold-out div.sqs-add-to-cart-button {
background-image: url(https://cdn.pixabay.com/photo/2023/09/26/17/32/woman-8277925_1280.jpg);
background-size: contain;
background-repeat: no-repeat;
background-position: center center;
}
Replace Pixabay with your custom button image url.