UPDATE
During the last two rides it happened that the bike did not respond to the throttle anymore. It helt the current speed but did not accelerate anymore. The gree GO was gone from the display.
After cruising to a halt in a safe spot and trying to reinitiate, the message "Side stand down" came up, so I knew it was the sensor. I wiggled it and I could go again.
Yesterday I dismantled sidestand and sensor and dared to open it (see pictures).
It is in fact a metallic contact switch actuated by a notched plastic wheel and not a hall sensor. Technology of yesterday

Manufacturer is LEONELLI of Spain and the sensor has the reference (type) number 063.
By my mishandling it, apparently the copper contacts were bent. I tried to rebend them, but I don't know if that is sustainable, so I am looking for a spare part.
An internet search found me that this sensor was also used for 1198 Ducatis MY2009-2011. Might also be installed in Aprilia 50 RS MY1999-2001.
The advantage of using the Ducati spare part is, that the connector appears to be the same as the original. I ordered the Duc sensor (50 Euro) and will report later if it fits as expected.