Just to complete my report, I’ve reported the issue here:
The erroneous wind speed was not really high (e.g. 7 km/h) but the air was definitely calm from end of rain through the night. One can tell the wind reading was wrong by observing gust-avg-lull. At certain points in time, they all matched. My other 3 stations did not report any wind. Even if I take into account the wind-cups inertia.