Custom Normals don't work on Displacement Modifier

Hey there!

I would like to have a mesh displacement along custom normals but it does not seem to work the way it should.
My custom normals look like this:

But the rendered displacement looks like this:

So it’s still basically using the vertex normals.
Doesn’t work either when I activate the modifier for the render.
The texture I use is full of white dots on black background.

Why is this the case? Can someone give me some advice?
Thank you!

In the subdivision modifier, go into the advanced tab and check “use custom normals”, or else the subdivision will override them.