How can one compute the Fichera norm of a function g \in H^{1/2}(\partial \Omega)? That is, the quantity

I think this might not be possible with dolfinx since ufl documentation says it can deal with this:

Don’t you think, it would be possible to first integrate over one boundary and then over the other?

Using stock Fenicsx UFL, this is not possible. I am also interested in similar types of boundary integrals (Fredholm types I and II), but at present there seems to be no straightforward way to do this. BEMPP was one way that you approach boundary integral problems with legacy Fenics, but I am not sure if they have a version that works with Fenicsx.

BEMPP works with FEniCSx, see for instance: Jupyter Notebook Viewer

Apparently, there is Fenicsx support for BEMPP. However, BEMPP only considers 2D surfaces in 3D, while my boundaries are in 1D, since I am solving 2D problems.

Did you only consider the 3D case so far?

Yes, I have only been working with 3-D problems.