Quick update on this thread: simply replacing the HVAC controller solved the issue, now I have heating, A/C, all functions work and the new unit did not burn down (yet). Thanks for all who commented and helped me finding a replacement!
I also replaced the connector because the original was mouldering, pieces broke off from it upon touch. It`s nice from Porsche to build a car that slowly disintegrates in about 20 years so it won`t be such a big burden for the environment. Very thoughtful.
Below is the original and the replacement is on top. The replacement is also used, but it`s somewhat newer, perhaps from 2002.
It also has this organizer/protector piece that slides in between the wires and help separating them. This part was missing on mine, which may have caused some sort of short and ended up burning down the circuit board.
Rebuilt connector.
