Display description of a product property

What “product property” do you mean?

It’s for the property of a taxonomy for products on this permalink: wp-admin/edit-tags.php?taxonomy=XXXX&post_type=product and one click of edit of a tag ->
https://www.barluxe.de/wp-admin/term.php?taxonomy=XXXXX&tag_ID=53&post_type=product&wp_http_referer=%2Fwp-admin%2Fedit-tags.php%3Ftaxonomy%3DXXXXXXXX%26post_type%3Dproduct

Its the textarea: term-description-wrap

Hope you understand it.

Display it in the Additional Information tab?

You can try this code:

function custom_wc_product_attribute_description( $text, $attribute, $values ) {
	if ( ! $attribute['is_taxonomy'] ) {
		return $text;
	}

	$items = array();

	foreach ( $values as $name ) {
		$term = get_term_by( 'name', $name, $attribute['name'] );

		$items[] = sprintf( '%s (%s)', $term->name, $term->description );
	}

	return implode( ', ', $items );
}

add_filter( 'woocommerce_attribute', 'custom_wc_product_attribute_description', 10, 3 );

Now you can just change this code for what fits you better.