Good question, it can be a little tricky to understand this but me try to simplify it.
First the emergency heat / aux heat setting you’re seeing in the device preferences page only applies to CT-xxx thermostat. It’s part of the CT thermostat settings section as it a special setting that supported by those models only (see CT manual for more details on how it works).
ZTS (remotec) Thermostats have their own settings section and it does not support any special configuration related to emergency/aux heating.
Coming to what you’re seeing in the logs, that’s why the thermostat is reporting to ST, it’s not configured to support emergency heating. Since it reports it as false, you won’t see that option when you toggle the modes. Typically you’ll see, heat, cool, auto and off. If the thermostat reports that’s it supports emergency then you’ll see an additional mode as you toggle through them.
You’ll have to refer to your thermostat manual to see how to enable emergency/aux heating mode. You may need to exlude and re pair your device with the hub after making the changes to your themostat before it reports to ST that it supports that mode.
It’s possible that the Remotec thermostats don’t report this mode to ST, it’ll handle turning on/off the multi stage heating internally as part of the regular Heat mode (it’ll use a temperature differential to turn on/off multi stage heating).