Replace "sold out" label with a custom image.

Add to Design > Custom CSS. Replace pixabay url with new image url

.product-mark.sold-out {
    color: transparent !important;
    background-image: url(https://cdn.pixabay.com/photo/2022/07/06/03/41/business-7304257__340.jpg) !important;
    background-color: transparent !important;
    background-position: center center !important;
    background-repeat: no-repeat !important;
    background-size: cover !important;
}