So, after several session of window adjustment and wait for rainy days, I have finally found what caused the problem for me. It was not the adjustment.
The issue was that due to the poor design of the whole mechanism, not only the guides collect a lot of dirt but also the front rubber guide of the window (that is part of the small fixed window, see attached pic). Any of these can make the window squeak in rainy days. Unfortunately, soaking with silicone did not help in my case, so I had to remove the fixed window, cleaned the rubber and the window (both were extremely dirty) and problem solved. I used 4-5 shop rags while the rubber got finally cleaned:
Btw, the newest iteration of the water seals (6th maybe?) is still rubbish. There was sleety rain some weeks ago and when I opened the frozen door, a lot of fur was removed from the seal by the frozen water ingress stuck between the seal and the window:
