Employers can only ask for the information for a 'specific purpose' - they would need to be able to justify what that purpose was. I would imagine that somewhere in the employment contract will be a condition about being able to meet the "entry requirements" of any countries they operate to and that would seem to be a justifiable reason. So if any require covid vaccination information as a condition of entry, failure to supply the information (or providing false information) would be a disiplinary matter.