hmm without seeing other config screens....
nzbget seems to be trying to write directly to your /mnt/user/tv-shows, it should be going to /mnt/user/download mainframe/completed/tv-shows where Sonarr can pick it up.
Also in nzbget/sonarr/radarr, the default setup has /downloads already setup and you just add the path. If you changed it to /data for all of them make sure Access Mode is read/write slave.
Somewhere you have a mismatch between them. Make sure your categories are the same for each and do you really need a remote port mapping if it is all within unraid?
*If you can post a screenshot of your unraid Sonarr docker config and also one of your nzbget settings/categories screen