I'm not sure that I understand what you are asking, since "prove that they have the insurance" seems to me to be equivalent to "telling the prospective employee

I'm not sure that I understand what you are asking, since "prove that they have the insurance" seems to me to be equivalent to "telling the prospective employee". Conceptually, I feel like there might be a connection to zero knowledge proofs (https://en.wikipedia.org/wiki/Zero-knowledge_proof https://en.wikipedia.org/wiki/Zero-knowledge_proof), so perhaps you can look there for inspiration if you haven't heard of it.