So I’ve made a few more attempts lately.
Now, when cutting, I simply lowered the laser by half the material thickness by 2 mm and left the kerf at 0.130 mm and lo and behold the results are significantly better:
In Y the deviation is larger. I assume that this is caused by the laser beam.
I think I can build on the results for further optimizations.
My thanks go to everyone who supported me with productive contributions.