All the fridge repair videos I have seen demonstrate how a fridge with a damper works -- in which case all the cooling happens in the freezer and a vent with configurable damper diverts some cold air to the fridge. Perhaps that is a US design.

European fridges are apparently different. The fridge and freezer are separate with no interconnecting vent. No fans either. The freezer is surrounded with coils embedded in the surface panels. The fridge has a plate with embedded tube for coolant. I am surprised that a plate the size of a large dinner plate/platter is big enough to cool the whole fridge.

The plate also has a tube in a loop of tubing that is not embedded into the plate but against it. The two ends of the tube join into a molding with 3 wires going to the thermostat (one of which is a ground wire). What is that thing?

There is a separate wire that goes to the thermostat. I think that is the probe that actually reacts to the temp.

I couldn’t easily send pics because the plate does not come off. I can barely pry it to get an eyeball behind it. I think everytime I bend the plate to see behind it I probably bend the tubes carrying coolant (not good).