This is mostly a note to myself if I ever want to figure out how I did this.
- Edit - configuration.yaml. I added a shell service:- shell_command: pikvm_power: "curl -X POST -k -u admin:super_secret_password https://pikvm-ip/api/atx/click?button=power"
- Reboot HA; needed for the - shell_command.pikvm_powerservice to appear.
- Add a button helper 
- Add an automation that calls the service when the helper button is pressed. 
Success!