@chris Ok so just called my friend who works in IT still, he said I was correct. The HR email was the source but it was sent to the department heads, who then disseminated it through the various department lists. The reason the email shows the email in the screenshot is because it is the "reply-to" address and not the from address.
I did some digging to try to find a screenshot of this and I found one, attached you can see the HR email but being routed through a list.
So my original point stands, he did not directly email them and did not even have their emails to be able to, he forwarded it to each department/organization head, disseminated it **through** them, but the reply-to is direct back to him.
The real scary part about this is it would allow elon to harvest the identity and email of government employees he wouldnt usually have access to (exemplified by this very process).