Meshing along a curve in 2D in fenicsx

I first define a square.

dish = gmsh.model.occ.addRectangle(0, 0, 0, L, W, tag=1)
arc = gmsh.model.occ.addCircle(0, 0, 0, r, tag=2)

How can I create a mesh along the circle that also mesh the arc of the circle?

It is unclear to me what you want to do. A sketch would be beneficial.
Do you want to mesh a square where a circle is embedded? If so you should use gmsh Boolean fragments, as shown in
https://jsdokken.com/dolfinx-tutorial/chapter3/em.html#meshing-a-complex-structure-with-subdomains

Please note that your example is incomplete, missing essential imports to make it reproducible. Please note that at the moment it is also a pure gmsh question.

As recently done for all other pure gmsh questions, I am going to close this and ask that you post your question at Issues · gmsh / gmsh · GitLab, i.e. gmsh support channel.