From some of the other comments, it seems like maybe the jellyfin server might be running on the desktop PC, in which case you can set the file permissions to be readable/writable by a group that both you and the jellyfin user are in.

You could potentially download to a mounted share drive via the desktop.

That is to say, set up an SMB server on the NAS and when you download music on the desktop, choose the SMB share as the download location.

It’s sorta goofy, but your LAN speed is almost certainly at least twice your internet speed.