Ok - it seems that I solved my problem somehow. After reading this on github https://github.com/prusa3d/Prusa-Firmware/issues/616
which describes partly the problems I have had, I went back to version 3.1.3. But that did not help at all.
Next I designed a new y-belt holder which is a bit longer and has longer screw holes so that I can shift it by 5 mm. I thought that if I shorten the distance from the end switch until the pinda probe is above the front reference point, I could solve the problem. The result was fail in xyz calibration.
Then I moved by rear v-profil of the bear-mod further back by 3 mm (just adding 2 3mm thick shims). The value for "Y distance from min" changed to 11.21mm left and 10.87mm right. The result for the test print was very unexpected - worse than before (picture Test2).
Then I decided to give the modified y-belt holder another try and shifted it towards the y end switch (completely). And all of a sudden it worked. The "Y distance from min" changed to 6.46 and 6.31. And the circles are round. (picture Test3). As one can see the print is still shift towards the y_min side.
I have not really understood yet why it is like it is but my feeling tells me that there is a virtual room defined somewhere in the firmware starting at the end switches. The xyz-calibration the determines by searching the 4 reference points where the head bed is located within this virtual printing room. And if calibration did not fail, the printer just stops moving towards one end of the head bed if it would move outside of the virtual room.
I could not find the definition these boundaries in the firmware. But I think it is somewhere defined. Maybe somebody of the developers could confirm that. At the end I'm fine for the moment.