show-alert-on-woocommerce-order-page.php

<?php
/**
**
** I like to prefix my functions, constants and variables in global scope 
** with YMCODE_/ymcode_ to prevent collision. Feel free to change it. 
**/

/**
** Set your custom message. Do not include html as it will be stripped off. 
**/ 
define('YMCODE_CUSTOM_MESSAGE', 'You have a special discount');

/**
** Set one or more categories IDs in the array. 
**/ 
define('YMCODE_CAT_IDS', [1,2, ]);


/**
**
** Add the popup code in JavaScript
**/ 
function ymcode_woocommerce_popup_alert()
{
	?>
	<script type="text/javascript">
		(function($) {
			alert('<?php echo esc_html(YMCODE_CUSTOM_MESSAGE); ?>');
		})( jQuery );
	</script>
	<?php
}

/**
** Check if cart has products from the categories mentioned above
**/
function ymcode_woocommerce_check_if_product_exists()
{
	global $woocommerce;
    $items = $woocommerce->cart->get_cart();

    $show_popup_alert = false; 

    foreach($items as $item => $values) { 
        $terms = get_the_terms( $values['data']->get_id(), 'product_cat' );
		foreach ($terms as $term) {
		    if (in_array($term->term_id, YMCODE_CAT_IDS))
		    {
		    	$show_popup_alert = true;
		    	break 2;
		    }
		}
    }

    if ( $show_popup_alert === true )
    {
    	//product exists, hook the javascript alert message
		add_action( 'wp_footer', 'ymcode_woocommerce_popup_alert' );
    } 

}

add_action('woocommerce_before_cart', 'ymcode_woocommerce_check_if_product_exists');

The corresponding blog post https://yakub.xyz/blog/2019/05/30/show-a-popup-on-woocommerce-cart-page-when-products-from-specific-categories-are-added/