yes your samba credentials are used to login to samba server. But this has nothing to do on how permission are set up on your system. As Samba did not support Unix file system permission, a local user is used to reflect this. Actually user dietpi is the one owning the share as you can see on your output.
However we setup Sonarr in a way to be able to write to folder owned by dietpi group. Could you check it pls
groups sonarr
sudo -u sonarr touch /mnt/jessica_tvshows/demo.file
ls -la /mnt/jessica_tvshows
This looks normal to me. User sonarr is able to write in the directory. Most likely sonarr has some other type of checking the write permissions, like the owner of the file. Could you try to add the same folder in sonarr and verify if the error persists?
That’s super weird now it seems to be working fine in Sonarr? I can’t say I’ve specifically changed anything though so who knows!
Thanks for your help…