By default, WordPress posts set to private are visible to admins, and you can distinguish them on the frontend because they have ‘Private:’ prepended to their title.
However, you might have plugins installed that are modifying this behaviour. It could be your capability management plugin, or it could be WooCommerce. The specifics of third-party plugins are off-topic here, so the best I can advise you is to disable these plugins one-by-one to see which causes it, and then ask at that plugin’s support forum for assistance.
In summary, the problem is most likely that a plugin is modifying default WordPress behaviour here.