id for categories and products

Try this, I have updated it with a hook for when you save the product, try saving a product and see if it assigns everything correctly

add_action('save_post_product', 'wpb_assign_product_to_categories_on_save');

function wpb_assign_product_to_categories_on_save($post_id) {
    // Check if this is a valid call
    if (defined('DOING_AUTOSAVE') && DOING_AUTOSAVE) 
        return;

    // Check the user's permissions
    if (!current_user_can('edit_post', $post_id))
        return;

    // Call the function to assign product to categories
    wpb_assign_product_to_matching_category($post_id);
}

function wpb_assign_product_to_matching_category($post_id) {
    // Retrieve the custom id for this product
    $product_custom_id = get_post_meta($post_id, 'custom_id', true);

    if (!empty($product_custom_id)) {
        $categories = get_terms(array(
            'taxonomy' => 'product_cat',
            'hide_empty' => false,
        ));

        $matching_category_ids = array();

        foreach ($categories as $category) {
            // Retrieve the custom id for this category
            $category_custom_id = get_term_meta($category->term_id, 'custom_id', true);

            // Check if the product's custom id matches the category's custom id
            if ($product_custom_id === $category_custom_id) {
                $matching_category_ids[] = $category->term_id;
            }
        }

        // Assign the product to the matching categories
        if (!empty($matching_category_ids)) {
            wp_set_post_terms($post_id, $matching_category_ids, 'product_cat');
        }
    }
}