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.
Why not? It's a public entity, with public employees and public property being checked out.
What if it was the Parks Dept. lending out chainsaws to the town's citizens. Could I get the log of people who signed out chainsaws?