The wording that matters, is that of the two Supreme Court rulings which I have referenced.
Garcetti v. Ceballos
" Judge O’Scannlain specially concurred. Agreeing that the panel’s decision was compelled by Circuit precedent, he nevertheless concluded Circuit law should be revisited and overruled. See id., at 1185. Judge O’Scannlain emphasized the distinction “between speech offered by a public employee acting as an employee carrying out his or her ordinary job duties and that spoken by an employee acting as a citizen expressing his or her personal views on disputed matters of public import.”
Id., at 1187. In his view, “when public employees speak in the course of carrying out their routine, required employment obligations, they have no personal interest in the content of that speech that gives rise to a First Amendment right.” Id., at 1189.
" Pickering provides a useful starting point in explaining the Court’s doctrine. ...
The Court found the teacher’s speech “neither [was] shown nor can be presumed to have in any way either impeded the teacher’s proper performance of his daily duties in the classroom or to have interfered with the regular operation of the schools generally.” "