I just finished my TDD-based REST API. And I would like to use Postman to document it for the frontend team until I realized it has its own test script. Now I'm wondering, is it necessary to double test it?
No there's nothing special about third party testing tools.
I would aim for the following in your tests
Automation. However you test the test have to run and report automatically. Without manual intervention.
Tests run the same way that its used. So if you have a client, test the api through the client, If you send out postman collections test with the postman collections
Keep test code small. Don't write a whole client and models just for your tests. Don't write complicated infrastructure to automate a third party tool