Hey,
It’s outside of the scope of this plugin and will require that you know php and are comfortable maintaining php files as woocommerce updates.
I can’t recommend that you do this. WooCommerce support is where you should be asking this question and they will tell you to hire a developer.
If you know php I can point you in the right direction, you need to move the email-order-details.php template into your child theme. Then edit lines 45 adding a new line for the category.
Then you need to move the email-order-items.php template into your child theme. Adding the call for category around line 74.
You could try some code like this:
<?php
if ( is_object( $product ) ) {
echo wc_get_product_category_list( $product->get_id(), ', ', '', '' );
}
?>
Ben