There is a plane, I would like to rotate this plane with e.g. 30 degrees, while the normal of the plane remains the same.

Furthermore, it has to be in a generic way, so the ‘original’ plane can take every position.
Below you find a ‘simple’ example of rotationg a XY plane. But is should also work for a plane in 3 dimension (present in attached GH file).

I don’t understand what you’re talking about…
What you see in the panel(rotated plane output)are the pieces of information of two plane’s origins and Normal vectors.
If you want to see the difference between the X-direction vectors of the original plane and the rotated plane, then you’ll have to use Deconstruct Plane and compare the angle difference using Angle.