Um, in this fantasy scenario of yours, who is doing this harassing and targeting?
The administrative bodies of Florida colleges and universities. That's not a stretch at all, I don't see why you think that is. I guess you're arguing that they would feel upward pressure from their faculty...
Poor guess. I'm arguing Judge Judy: "It doesn't make sense, and what doesn't make sense isn't true."
In this fantasy scenario of yours, what are the political leanings of the administrative bodies of Florida colleges and universities and what are the political leanings of the professors they're harassing and targeting? Rightist and leftist, respectively, since you seem to think the point is "creating an avenue for the culling of leftist professors"? So, first off, what evidence is there that the administrative bodies of Florida colleges and universities are populated by rightists?
Second, even if we accept the dubious assumption that the administrative bodies are made up of conservatives intent on culling progressives, and to do this they need a list of progressives, then what is their motivation for writing a survey that says answering is optional and the survey is confidential, if they intend to get that list by harassment and threats against the decline-to-answers? To do that would be to drop the facade that the survey is confidential. So why adopt the facade in the first place when all it can accomplish is to make them look like liars?
And in the third place, what is the motivation for all these leftist professors who initially refuse to answer the survey questions to react to the harassment by knuckling under to the invasion of their privacy and complying with the unconstitutional demand and saying "Okay, okay, I'll tell you. I'm a leftist."
to an administrative body intent on culling leftist professors? That sounds like a wholly ineffective tactic for keeping their jobs. Consequently, harassing professors to state their views sounds like a wholly ineffective tactic for culling leftist professors. So why would the administrative bodies deliberately choose that tactic?
Your scenario's story doesn't hang together. Maybe the survey is an element of a sinister plan to cull leftists and maybe it isn't; but either way, it evidently is not "requiring FL students, professors to register political views with state".