It should seem obvious that they do need to be proxi aligned.
The modules all around the car need to know how to communicate with each other this is what the proxialignment does it tells all other modules that this is the climate control unit and this is how to address it on the network.
Is the new climate module definitely from the same year and model of stilo, as one thing that can cause it to fail is if the part is much newer than the car, the car has never been fitted with the software within the modules needed to address a much newer mode of climate unit.
The other possibility is that, often proxialignments can fail or be very temperamental so it might mean you need to try it many multiple times and fiddle about with things before it finally works.
What was the issue with the old climate module