From a philosophical perspective, I don't see how the vaccine mandates for public jobs is appreciably different than vaccine requirements for public school that already exist.
As far as the China lab goes, there were plenty of scientific papers that studied the China leak theory, though I personally don't know what they found.
The difference between the vaccines you're talking about lies in their development time: The one in school have been (tested) around for decades before getting mandatory.
The COVID vaccines have now been around for 4 years now, and there is no evidence they are appreciably more dangerous than those other vaccines that took longer to develop.
As far as the China lab goes, there were plenty of scientific papers that studied the China leak theory, though I personally don't know what they found.