Does the First Amendment apply to government speech such that defamatory government speech is protected free speech?

QUESTION PRESENTED The questions presented are: 1. Does the First Amendment to the United States Constitution apply to government speech, such that defamatory government speech constitutes an act in furtherance of of a right to free speech under the United States Constitution? 2. Does government speech become “protected speech” under the First Amendment to the United States Constitution solely on the basis that the target of the defamatory speech is a public figure? 3. If the criteria in New York Times v. Sullivan apply to the circumstances of this case such that constitutional protections for speech and press limit the state court’s power to award damages in a libel action brought by a public official against a government employee speaking in the course and scope of his government position, does it also divest the public official of any remedy whatsoever, including the right to seek a judgment from the Court that the speech at issue was defamatory?