Okay, I had 5 minutes so I had a look.
I took my spare ASR-ZW, added it to ST as a thing and it gets detected and added as a Z-Wave switch by ST.
Using the default device handler and turning the switch on and off does nothing.
A quick search revealed this post which states:
According to their documentation, it uses the Thermostat device classes, so it should work in ST with the default thermostat device handler.
So I went in the IDE and changed the device type to Z-Wave Thermostat. That allowed me (in a roundabout way using one of the thermostat buttons) to turn the ASR-ZW on and off. Which in turn means you could control it with CoRE.
It really needs the default z-wave thermostat DH changing so that this simple on/off device can be controlled.
Suggest you also read this:
Hope that helps!