Unless it's like, air gapped powered by a naval nuclear reactor, I feel like someone would question why a random US gov building is drawing 20-30MW of power, and exhausting most of that as heat...

Aside from the utility, who would know? There's a lot of land out there, relative to the size of even a very large building.

Not disagreeing with you but how could any building draw power without radiating most of it as heat?

How do you tell the difference between a datacenter and a supercomputer cluster? According to wikipedia, the government data center in Utah is pulling 65 MW.

The DOE has entered the chat.

(after the nuclear test ban treaty, they run a LOT of simulations)

Isn't that the open secret for El Cap? "Classified workloads" aka weapons sims.

Not a secret, from IEEE:

The NNSA—which oversees Lawrence Livermore as well as Los Alamos National Laboratory and Sandia National Laboratories—plans to use El Capitan to “model and predict nuclear weapon performance, aging effects, and safety,”

There's no real secret about nuclear weapons simulations. Sure the software they use is protected and "secret", but the real secret computing facilities are likely there to break encryption and spy on everyone. Nuclear weapons simulations don't really give the US a tactical advantage, but breaking encryption does, and so that kind of compute power would be kept secret.