Who know's about unspeakables?
I assume their work is basically treated like 'classified' work in the modern era - so some people in government know what they are up to.

Just the Minister for magic? Just Cabinet members? Senior wizengemot - or might some items be referred to the experimental committees depending on what acutally is being researched.

I assume there would be occaisions when some of the classified work is declassified if it's in the public interest or suitably developed into something usable and safe for the public.