Creating normal textures from procedural textures has allways been a bit difficult in Cycles… As sampling is done in tiny fractions of a pixel, the values produced by the procedural textures can vary from sample to sample, making the resulting derivative difficult to converge.
Using the Bump node, one needs to be carefull when choosing the correct distance (the default 1.0, is way too big for a procedural texture; i tend to go around 0.005 but it depends on the size of the height variations). And a strength of 1.0 is also a bit big (a value below 0.5 is normally better).
Another option is to bake the procedural texture, and use the texture with the Bump node. This works quite well, but it’s an extra step.
For the NormalMap node, we need a different setup (the one you used)… That’s because the colors from a procedural texture don’t quite represent the encoded Normal vector direction, and a small adjustment is needed (all that vector math), so that the resulting normal vector lands in an acceptable range.
I used a similar construct here (file included), and it’s been my preferable method for years.
As for Displacement/Bump, I never use it, except when I really have geometric displacement.