I can go to the Property Appraiser's office and find out everyone who's ever owned my house and what they paid for it.
I can also go to any public agency and ask, by name, what their salary is. To a point, I can even get their employment record.
I can go to the police station and look at the arrest blotter and find the names and addresses of the folks arrested.
I can look up divorce records at the courthouse. Find names, property divsions, etc.
So in an open records state like FL, why should I not be able to find out the check-out record of a publicly owned book in the library?
Setting aside asking about public employees' job details -- that wouldn't apply to a private employee -- everything you list is a legal transaction or, in the case of the property appraiser, has to do with taxation. Borrowing a library book isn't.