This unit file worked for me. Changed the config path in ExecStart, and added Environment directive containing path to esphome binary.
[Unit]
Description=Esphome Dashboard
After=network-online.target
[Service]
Environment="PATH=/srv/esphome/bin:/home/homeassistant/.local/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"
Type=simple
User=%i
WorkingDirectory=/home/%i/.homeassistant/esphome
ExecStart=/srv/esphome/bin/esphome /home/%i/.homeassistant/esphome/ dashboard
[Install]
WantedBy=multi-user.target