First, there’s this:
https://www.cdc.gov/vaccines/programs/iis/downloads/basics-immun-info-sys-iis-508.pdf
Second, if you can provide proof of your vaccination to your employer, which you can, and your employer can verify that information, which they can, it goes without saying the information connecting you to a particular batch, lot and vial is known and could easily be passed back to the pharmaceutical company. That pharmaceutical company then needs only do a little work to find out what your subsequent interactions with medical providers were.
Remember, you agreed to be part of a medical experiment. What is being tested and what data is being collected is really none of your business. After all, they provided you with the contents of that vial for free. You agreed not to care about what was in it.
Very salient points.
