>Public property is another story, and a bit stickier.
No kidding; especially public *government* property.
One interesting thing I found (after asking “what authority/authorization does the [State’s District] Court have to say ‘No Unauthorized Weapons, violators will be prosecuted’” after seeing that posted on the courthouse when I reported for Jury Duty) is that there exists no actual law barring weapons from the courthouse. {What they do have is a “court rules” document which specifies it; however, the State Constitution says “No law shall abridge the right of the citizen to keep and bear arms for security and defense [...]” so any prosecution thereof would be just such an abridging law.}
Well, I did say that bearing arms on public property is "sticky".
As your example above shows, a citizen would be well within their constitutional rights to go armed inside the courthouse --- but, you'd better be prepared to go through all sorts of hell to defend that right, should you do so.