I have a Honeywell T6 Thermostat with Z-wave integrated into homekit. I can manually put the unit in on/off/auto without any issues. I have noticed that via automation I can turn off the unit, but I cannot turn it back on via automation, even when doing test this automation or having the automation run, it will not put the unit in the on or auto status.
I just yesterday installed 2 of these to replace my old Ecobees! I haven't gotten to automations yet, but I did have an issue with the parameter: thermostatMode. There doesn't appear to be an auto option, so I've had to manually set it to get other settings working.
E.g., mode was heat last night, and even though temperature rose above cooling set point today, had to manually set that to cool.
This may not have anything to do with your issue, but I'll definitely report in as I get a better feel on these and do some automations.