Add overlay images for new and sold out products on the product list pages in WooCommerce.

functions.php

<?php

class shopTheme {
  	public function __construct () {
	  	/* Add overlay images for products in shop list */
		add_action('woocommerce_before_shop_loop_item_title', array($this , 'add_overlay_images'), 10);
	}

	/* Add overlay images for products in shop list*/
	public function add_overlay_images(){
		global $product;
    
    		//If product is in stock
		if ( $product-> is_in_stock() ) {
      			//If the product was created less than 30 days ago, echo image for new product
			if ( strtotime( $post->post_date ) > strtotime( '-30 days' )){
		    		echo '<img src="new.png" alt="New product" class="new" />';
		    	}
		} else {
			echo '<img src="sold-out.png" alt="Sold out" class="sold-out" />';
		}
	}
}

new shopTheme();