I am constantly subjected to baseless investigations by my university. Here's my story.
And the moral of the story is: In your role as a professional intellectual, do not publish on a platform that was explicitly created to limit the amount one can say to less than that required to state a pair of premises and a conclusion.
Hard to feel a lot of sympathy here. You tell a junior person they shouldn't annoy people in power because it will be bad for their careers, then play the victim because people more senior than you get annoyed with you and threaten your career.
sorry dude-- as much as i hate to side with university admin on pretty much anything, i have to say that the ex cathedra tweet definitely reads as menacing.