It is working. Finally. There is still one issue, but that is hopefully harmless compared to the rest. I have to check how far the car is from the center of the track to find out if the car left the track. In that case I will reduce the speed to 0 and put the car back into the middle of the road.
The last few problems were all more or less stupid errors. The first was that the car didn't lean into the curve. I looked at the normal which was calculated and it was mirrored, so the car was leaning into a left curve when the track made a right curve. The reason behind that was that a function evaluated the track in the wrong direction.
The second big one was, that the car didn't follow the track, but moved under and over the track. It turned out to be another stupid error. The position of the car I get by intersecting planes with the down vector, but the planes had the wrong normal. In a place I switch cosine and sine with the result that the planes had an inclination of 45° (using twice cosine to rotate a coordinate system) while the track was only 5°.
So now the car finally moves with the track. Next is the issue from above and then I will work on a different area, I will add the ability to brake to the program and also handle potential energy so the car decelerates when going uphill and accelerates downhill.