I’ve known people with clearances at Govt contractors. They could say what they do, EE/ME for X project but not many details beside that.
It's like this for many gov agencies working with intelligence because labeling yourself as an intelligence worker makes you a target for foreign intelligence agents.
That may sound a little strange if you aren't part of that industry, but it is the truth.
I don't think this is as absolute as you make it sound. Plenty of NSA employees have published papers using their real names in conjunction with nsa.gov or ncsc.mil email addresses
What do the folks in Virginia say to their neighbors? “Oh I work for the DOD. So your a spy right haha?”
That seems like a difficult to keep secret