If I understand correctly, you perform a project export - or attempt to - yet no file is delivered? Do you see an error on the project? I ask because it appears that export failures aren’t communicated well (SONAR-10741). Also, do you see anything in your server logs?
And to answer your question, there’s not currently a way to download the file via APIs. We’ve got tickets in for that though (SONAR-10753, SONAR-10774, SONAR-10768).
Quite some time has passed since the original discussion on this topic. I am experiencing the same situation as Fangfang had 7 years ago: I want to export projects via the API.
My SonarQube version is Enterprise 2025.1.1. The token I am using is a user token owned by a user with all available permissions, including Administer System.
However, I am not getting the expected result. The project is not exported. The http response code is 400.