They probably aren’t themselves, but they probably do have a contract with a private company so they can keep it secret. Anything the government does would have a record, unless the work is contracted out to a private company.
Like Lockheed Martin and building secret aircrafts for the military. You can see the budget but you cant get details of what they are doing. You cant FOIA request for information from a private company
Someone should submit a FOIA asking for all information on The US government mining bitcoin. Be interesting if you got back a bunch of redacted documents back. Would be interesting just to see what they say.