The power being provided to the unit is just a side effect. More than likely 24vdc and a set of contacts. If you were to wire a simple toggle switch in and flip it on the heat would turn on.

I’ve dealt with hundreds of thermostats they all work in a similar fashion the new ones just use multiple relays with a single power wire. The old school thermostats just used bimetal contacts or clock springs with a mercury relay. Modern ones use electromechanical or solid state relays. This includes things like the nest thermostats.

An ESP8266 running ESPHome and a relay would work here. It’s basically on or off. Then you could pull temperature information in from multiple temp sensors around your home.

I do something similar for some solar air heaters I built.

I actually started using HomeAssistant on TrueNAS Core a few years ago. From my understanding the best way to do this now it’s to use the TrueNAS X86-64 ISO in a VM. The TrueNAS docker system seems to be integrated differently than a standard docker installation on an os like Debian.

If you really want to keep using docker on TrueNAS you should create users with unique ID’s in TrueNAS and give them permission to access the needed resources. Those ID’s also need to match the user in the Docker container.

I personally use HomeAssistant on an Odroid N2+ and haven’t made the switch to TrueNAS Scale so I can’t be much help beyond that.