Have you had experience automating API testing with scripts in Postman?

Yes, in Postman, it is possible to automate API testing using the built-in scripting engine based on JavaScript. Scripts are written in the "Pre-request Script" and "Tests" sections to prepare the request and verify the response, respectively.

Example of a simple test in Postman that checks if the response status is 200 and the body contains the field "success":

pm.test("Response status is 200", function () {
    pm.response.to.have.status(200);
});

pm.test("Response contains success", function () {
    var jsonData = pm.response.json();
    pm.expect(jsonData.success).to.eql(true);
});

Such scripts allow automating the verification of API correctness, running tests in collections, and integrating with CI/CD systems.