I usually generate an API client in C#, and just use that. For example, and entire integration CRUD test for a user would just be something like:

var user = TestClient.CreateUser(1234, "Bob");
user.Id.ShouldBe(1234);
user.Name.ShouldBe("Bob");

var userThroughGet = TestClient.GetUser(1234);
userThroughGet.ShouldNotBeNull();

TestClient.EditUser(1234, "John");
userThroughGet = TestClient.GetUser(1234);
userThroughGet.Name.ShouldBe("John");

TestClient.DeleteUser(1234);
userThroughGet = TestClient.GetUser(1234);
userThroughGet.ShouldBeNull();

Trying to set up those kinda scenarios quickly with Postman was getting pretty tedious