I don't know what I am doing, but from a quick test, the mail header is at least disclosing the internal recipient (mail@host.com) "translation address" (as mail_at_host_com_12345abc_12345abc@icloud.com) and an alias creation date. But the latter seems to be a unix timestamp related to the real address alias creation time and is identical between an hidemyemail mail and a normal one, so there may be already a possible information leak for correlation. Side note, it also seems like the sending hidemyemail server contains the unsuspicious name "junk_forwarder". Lol.

Disclosing an address as alias and particularly as throwaway alias (through the translation address and server) already seems kinda counterproductive to begin with, but I would bet you can use this information somehow to get the sender "translation address". Either by some API interaction, or by messing with the mail header scrubbing of the translation service somehow. A server named "junk_forwarder" may be a little more lenient about what to accept or not.

Edit: Can confirm the Reddit comment linked. You simply send an email to the HME address, reply from Apple mail client, and then the real mail address gets disclosed. Mind you not even hidden. It's shown as sending from the HME alias in mail, but I received the mail with the real address as sender......... Jesus fucking christ, Apple. Did you even test this a little?