No this functionality is not supported and maybe a minor bug that it looks like it is?
To do this operation you can use the “Reveal in explorer” funtion by right clicking the file/ folder you want to move. You can now carry this out in windows explorer.
Drag and drop is only for loading files, not moving them around.
Renoise Diskbrowser was not meant to mimic file explorer environments.
I personally even consider the waste-basket unnessesary but that is a personal opinion, there are folks that probably use this option.