In default setup Transmission run as the user transmission.
About how you can improve.
Look, what rights to the directory in which you're trying to swing.
Stop the daemon
sudo systemctl stop transmission-daemon.service
sudo systemctl edit transmission-daemon.service
Write something like:
Change the permissions of the directory data:
sudo chown toilay:twoup -R /var/lib/transmission-daemon
sudo systemctl start transmission-daemon.service
I currentcatalog on Filipovich create a separate user, it is indicate in the settings of the samba server.
It turns out that the fix is fine, and the files writable.