With current Media Writer v5.1.1 on Linux, selecting Download automatically and then Spins does not give the option of Fedora Budgie Desktop, nor is it anywhere else.
Manually downloading Fedora-Budgie-Live-x86_64-40-1.14.iso and then using Media Writer to create an USB bootable media works correctly as expected.
With current Media Writer v5.1.1 on Linux, selecting Download automatically and then Spins does not give the option of Fedora Budgie Desktop, nor is it anywhere else.
Manually downloading
Fedora-Budgie-Live-x86_64-40-1.14.iso
and then using Media Writer to create an USB bootable media works correctly as expected.