As far as I can find, in the US and the UK, conditions of entry to a business are considered an implied license and not an implied contract because there's no mutual intent to form a binding legal agreement. A business can revoke the license and trespass you, but they cannot sue you for breach of contract.

A unilateral contract requires some kind of "promise accepted through performance"

I note that this does appear to be different under Australian law, if that is where you're from, although it's still not a unilateral contract.