The package is most certainly broken and I cannot get tvheadend to come up using systemd but I can get it to work as a daemon which means you can start it via ssh and then log out and it will stay up.
This might see you through until I/you/someone else can fix the systemd service;
Clear down the current config for your CURRENT and tvheadend users;
sudo rm -rf /home/tvheadend/.hts
sudo rm -rf /home/YOURUSERNAME/.hts
Start the tvheadend binary in 'firstrun' mode using your real login using;
tvheadend -C
Kill the tvheadend binary (CTRL+C) - no need to do any config at this point
Move the config directory from your current user to the tvheadend user;
sudo cp -R /home/YOURUSER/.hts /home/tvheadend
Fix the permissions on the .hts directory;
chown -R tvheadend:tvheadend /home/tvheadend/.hts
Start tvheadend with the following command;
/bin/tvheadend -f -p /var/run/tvheadend.pid -c /home/tvheadend/.hts/tvheadend -u tvheadend -g tvheadend -6 --http_port 9981 --htsp_port 9982
You should then see tvheadend running on
http://YOURIP:9981 and be able to access the webui without a username/password. Then create a user and matching password and then you can log in.