All you're doing here is arguing with yourself: you agree that the barrel of a gun is, in the final analysis, ultimately used to enforce both vaccine mandates and private contracts. Therefore an opposition to things being enforced at the barrel of a gun alone is an incoherent reason to oppose vaccine mandates and not private property.
Honestly, I’m not sure what point you are arguing here, let alone what you think I am arguing. I’m certainly not opposed to mandates solely because they’re enforced at the barrel of the gun (because yes, obviously that is every law in existence). But since we’ve clearly lost the thread or perhaps we’re mixing each other up, let’s just call it a day.