Hi,
many thanks for your request. In general just plug the USB stick to your device will not make it usable / available. For this you would need to mount the stick. This can be done using DietPi Drive Manager. Next to that I would recommend to use ext4 instead of exfat as this could lead to issues on renaming files using Sonarr. See link below.
https://dietpi.com/forum/t/sonarr-cant-move-rename-files/3550/13