All requests which are using the microservice proxy {{url}}/service/{{microservice_name}}/health (etc.) require authentication.
If you have the possibility on the edge to not use the proxy but internal APIs (like http://cumulocity:8111) the health endpoint does not require authentication but will show less information as property management.endpoint.health.show-details=when_authorized is used.
Not sure though if cumulocity 8111 is exposed on the edge. You can give it a try but this will only work edge internal.