No. That way, you are moving the tv-shows folder and rename it ToDo inside /srv/mergerfs/Media/
What you want is to move files that are inside tv-shows and have them inside the ToDo folder, correct?
mv /srv/dev-disk-by-uuid-ebc5282d-580c-4b97-ba3b-5b1beba70312/Leeching/Leeching-Done/tv-shows/* /srv/mergerfs/Media/Media/ToDo/
You better read about the mv command since it doesn't have the same flags as rsync.
mv(1): move files - Linux man page (die.net)
Try first with 1 file and check if permissions are maintained.
mv -v /srv/dev-disk-by-uuid-ebc5282d-580c-4b97-ba3b-5b1beba70312/Leeching/Leeching-Done/tv-shows/<A FILE NAME.MKV> /srv/mergerfs/Media/Media/ToDo/
ls -al /srv/mergerfs/Media/Media/ToDo/