Is the idling instability of the new Jetta related to the water temperature sensor?

This is the corrected signal after startup.

It's not usually the problem.

Idle speed instability is usually due to

Auxiliary air conditioner

The intake pipe is blocked or leaked.

air metre

revolution speed transducer

Fuel injector problem (blockage)

Fuel pressure regulator

Oil pump oil supply problem

Weak ignition

Spark plug