That wasn't my point. In fact, I agree with what you're saying.
But what happened with the covid vaccination was, firstly, that the State mandated it, either explicitly, or indirectly by discriminating against those who did not take it, including companies. The degree to which each of those happened depended on the jurisdiction.
Second, and more to the point that we're discussing, forget about the written contract then. There was no "and you will take experimental vaccines if I tell you so" condition of employment. So there had been no agreement, and unilaterally breaking an agreement is punishable, State or no State. In a free society, there would still be enforcement. In a variety of ways that can range from physical to merely reputational.
In any case, you cannot make an abstraction and move to the ideal libertarian scenario what happened to millions upon millions of real people in the actual conditions of 2020-2022. In those, the State is there to enforce contracts, and my position is that vaccine mandates are a flagrant breach that should be legally prosecutable.