Earlier quoted context omitted.
Governments do have free speech rights. Those rights may be limited compared to the rights of private citizens, but they do exist.
Democratic governments have privileges bestowed on them by their constituences. I don't remember where the US Constitution gives any branch of government "free speech" rights. It definitely has some protections for speech of officials in Congress and in courts. Authoritarian governments, of course, have all the rights they manage to grab. Look what Russian officials say. I suppose that North Korean officials can say…
The government is protected for speech related to its duties, in clearly spelled out ways.