Costs for indoor railings / handrails in order - experiences?

That is out of the question for me, nothing was said about it to the railing builder either.

I also had the problem with the bent barrel.

Can someone explain why this is, even though the step height is the same.

That is due to the different step depths. The height of the individual steps is the same, but the distances over which this height has to be overcome vary.

I hope that is somewhat understandable?

I also really wanted a straight handrail and only gave in when we were shown with the slat: at the lowest point, a child could have easily climbed over with us. If you adjust the height to this lowest point, however, it becomes too high at the highest point.
In addition, at my parents' house, a straight handrail is installed on the U-staircase, and I have personally experienced how annoying the feeling can be when the hand "wanders" in height compared to the shoulder when running along it.

Note: we have a U-staircase (half-turned?), how much this affects a two-times 1/4 turn staircase would have to be seen.