I think you need to question what should the Postman tests cover. Just because it is a requirement, does not necessarily mean it makes sense and it is a good idea.
Postman does not interact with your code, it interacts with the API that the application exposes. As Postman does not have access to the code directly, it cannot report back which code was executed.
Code coverage is usually a requirement that applies to unit testing or similar tests that are executed directly on the code.
Postman is an API testing tool, it implicitly tests how the entire system made of components works together.
So unit testing / API testing (or integration testing) are two different things with different purposes.