Are you sure about this? Are you an attorney? I am not.
I ask because it was my impression that, more than each individual having a right to free speech, each individual has a right to be free from a certain set of governmental restrictions or punishments for their speech, and that this is also true of the non-governmental-employer-employee relationship, but the set is smaller.
For instance, it was my impression that:
(A) People who are not governmental employees have the right to be free from the government restricting them from criticizing Congress in most locations at most times (and have the right to be free from the government punishing them for this criticism)
(B) Governmental employees have fewer rights that (A) in certain respects related to their employment
(C) People who are non-governmental employees can generally be fired for their speech, though not for certain speech, like stating that she is pregnant or whistleblowing to the federal government (under some circumstances)
But I am not a lawyer.