I have finally found the solution!
Everything is fine with the car! It is working as intended.
I was just thrown by the finer details of voice control (my bad).

The voice control in the Jazz works like this (it is a bit obscure in the manual):
* use a
short press for "normal" built-in voice commands
* a
long press (actually not so long as I've found out) will activate the voice assistant of a coupled smartphone
As I have no phone coupled to the car there are no voice commands available on a "long" press.