I could agree with you, as long as we can also agree then that an employer has legitimate right to demand from their employees things like sexual services, or that they eat a specific diet, or that they vote a specific political candidate, or that they amputate a part of their body, or that they give them the keys to their homes, or to their bitcoin wallet.

If we can establish that such a contract is legitimate, then yes, demanding vaccination is also legitimate.

The catch here though is that I'm conditioning all these to being known and discussed in advance, clearly stated on the employment contract, and thus "freely accepted" for real.

Which is NOT what happened during covid to most people who were the victims of a unilateral, non-negotiable alteration of their employment contract.