Add custom ID attribute to all woocommerce products on archive pages

Copy /woocommerce/templates/content-product.php to /yourtheme/woocommerce/content-product.php and modify it as needed.

In this case, we can change the opening <li> tag from this:

<li <?php post_class(); ?>>

to this:

<li <?php post_class(); ?> id="<?php echo esc_attr( 'post-' . get_the_ID() ); ?>">

The updated content-product.php file will look like this:

<?php
/**
 * The template for displaying product content within loops
 *
 * This template can be overridden by copying it to yourtheme/woocommerce/content-product.php.
 *
 * HOWEVER, on occasion WooCommerce will need to update template files and you
 * (the theme developer) will need to copy the new files to your theme to
 * maintain compatibility. We try to do this as little as possible, but it does
 * happen. When this occurs the version of the template file will be bumped and
 * the readme will list any important changes.
 *
 * @see     https://docs.woocommerce.com/document/template-structure/
 * @author  WooThemes
 * @package WooCommerce/Templates
 * @version 3.0.0
 */

if ( ! defined( 'ABSPATH' ) ) {
    exit; // Exit if accessed directly
}

global $product;

// Ensure visibility
if ( empty( $product ) || ! $product->is_visible() ) {
    return;
}
?>
<li <?php post_class(); ?> id="<?php echo esc_attr( 'post-' . get_the_ID() ); ?>">
    <?php
    /**
     * woocommerce_before_shop_loop_item hook.
     *
     * @hooked woocommerce_template_loop_product_link_open - 10
     */
    do_action( 'woocommerce_before_shop_loop_item' );

    /**
     * woocommerce_before_shop_loop_item_title hook.
     *
     * @hooked woocommerce_show_product_loop_sale_flash - 10
     * @hooked woocommerce_template_loop_product_thumbnail - 10
     */
    do_action( 'woocommerce_before_shop_loop_item_title' );

    /**
     * woocommerce_shop_loop_item_title hook.
     *
     * @hooked woocommerce_template_loop_product_title - 10
     */
    do_action( 'woocommerce_shop_loop_item_title' );

    /**
     * woocommerce_after_shop_loop_item_title hook.
     *
     * @hooked woocommerce_template_loop_rating - 5
     * @hooked woocommerce_template_loop_price - 10
     */
    do_action( 'woocommerce_after_shop_loop_item_title' );

    /**
     * woocommerce_after_shop_loop_item hook.
     *
     * @hooked woocommerce_template_loop_product_link_close - 5
     * @hooked woocommerce_template_loop_add_to_cart - 10
     */
    do_action( 'woocommerce_after_shop_loop_item' );
    ?>
</li>