I think you are mistaken. The University of Central Florida is a government institution, through and through.
They may not be jailing him, but they clearly were punishing him, specifically for making First Amendment Protected statements on his own time, off the job.
It does say “Congress”.
So, I’m afraid the “First Amend” cries common all these years are a bit misplaced.
The principle is nice - but then, that is also what forces you to retain trannies and all that garbage. It goes both ways.
Never mind though many colleges are state institutions, or funded, they still should have a right at some point.
I think sticking to courts is the best way to go, for judgement on whether it was excessive, which he did.