I have been working on the same problem myself and I just found a solution.
Complete lack of documentation on this feature but I got it working using the REPL API. In the Easi> web interface under configuration, make sure httpd is set to no TLS, no authorization for the following commands to work.
#Set Pin 0 High
curl -X PUT http://192.168.1.136/api/v1/repl -d "io -h 0"
#Set Pin 0 Low
curl -X PUT http://192.168.1.136/api/v1/repl -d "io -l 0"
Then translate that into your Home Assistant configuration.yaml file:
shell_command:
central_heating_on: curl -X PUT http://192.168.1.136/api/v1/repl -d "io -h 0"
central_heating_off: curl -X PUT http://192.168.1.136/api/v1/repl -d "io -l 0"
Depending on your relay type you made need Low for ON, so adjust the commands accordingly. I hope that helps!