I found an API through the QTest backend call for exporting the test cases to Excel.
Ex: https://qtestnet.com/p/11111/portal/testdesign/export/testcase.
But this is not working either through postman or Java. I feel like this is an internal API, not being exposed to the public. Kindly let me know if there is another API for exporting test cases from QTest.
you can try using the qTest api to get data and write to excel.
https://github.com/ryan-rs/qtest-swagger-client
It's in python so I'm not sure if this is what you're looking for but I have been able to get data from qtest and export to qtest via this api.