Thank you for your answer!
I did check the log files of my server and the request was listed there. The browser (or browsers; I did try Chrome and Firefox and both do have the same problem) did send the request and receive the response. But the browser does log nothing into console or network traffic.
Firefox did just display a blank page and even prevented reloading the page. Chrome did also display a blank page, but reloading was possible and did trigger the download. But as soon as I did start network analasys in Firefox, the download was triggered, too.
It seems that this is a browser issue. I hope it will be fixed soon.