2017 Western Star 5700xe Webasto Heater

Batteries are in the side under driver I think. Do you have a battery disconnect switch under driver seat area? To reset system?

 

No kill switch in a freightliner product from recent years is weird.

 

It is a standard fearure to protect batteries when parked for extended periods.

 

Did you buy from one of those guys with the Singh last name?

 

Back then, I believe the manual cutoff switch was an option on the O/OP spec.
I am assuming this is a factory heater install? Did you remove the cover to expose the heater itself?
My 2015 Coronado (factory, not glider) though different cab than your 5700, has the sleeper protection behind the trim plastic at the drivers seat belt pillar. (sorry for lack of better words to describe)
Your refrigerator comment makes it sound like a connector issue behind the panel that has the dial. But also, you should be able to find the heater power supply routing on the heater's site. "IF" I recall correctly, the power goes to the heater first, then to the controller and back to the heater. The controller is just a thermostat with small wires. So I would pull the cover to expose the heater unit and find that connector, then pull the panel that has the control dial.
Since the dial lights up when the frig switch is hit, then power is still active, IMO, but not returning to the heater. In 2017, this heater should still be a non integrated system.....I think anyway. So the heater brand customer service might also be of help. Believe it or not, and I think I have mentioned this on this site in the past, I have had great luck with the component brand customer service on both my PACCAR and Daimler products.