You could modify the service file /lib/systemd/system/dropbear.service
and change the ExecStart= line to
ExecStart=/bin/sh -c '/usr/sbin/dropbear -EF -p "$DROPBEAR_PORT" -W "$DROPBEAR_RECEIVE_WINDOW" $DROPBEAR_EXTRA_ARGS 2>&1 | tee -a /var/log/dropbear.log | logger -t dropbear'
Which should log everything also into /var/log/dropbear.log. (I did not test this and of cource you can change the path to your likings)
Don’t forget afterwards:
sudo systemctl daemon-reload
sudo systemctl restart dropbear