Want to import already defined physical groups of Microstructure in Gmsh to FEnics

mesh
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As Francesco said, the latter bit of the tutorial uses the data from gmsh directly.
The tags are read in with

with XDMFFile(MPI.COMM_WORLD, "mesh.xdmf", "r") as xdmf:
    mesh = xdmf.read_mesh(name="Grid")
    ct = xdmf.read_meshtags(mesh, name="Grid")
mesh.topology.create_connectivity(mesh.topology.dim, mesh.topology.dim - 1)
with XDMFFile(MPI.COMM_WORLD, "mt.xdmf", "r") as xdmf:
    ft = xdmf.read_meshtags(mesh, name="Grid")

and then converted to a dolfinx.fem.Function with:

Q = FunctionSpace(mesh, ("DG", 0))
kappa = Function(Q)
bottom_cells = ct.find(bottom_marker)
kappa.x.array[bottom_cells] = np.full_like(bottom_cells, bottom_marker, dtype=default_scalar_type)
top_cells = ct.find(top_marker)
kappa.x.array[top_cells] = np.full_like(top_cells, top_marker, dtype=default_scalar_type)

In summary, you just need to transfer the data from a MeshTags (in legacy dolfin MeshFunction) to a Function if you want to use the values of the markers in your variational form as parameters.

There are other ways of defining these sub domains (although I rarely use it), see for instance: https://fenicsproject.org/olddocs/dolfin/latest/python/demos/subdomains-poisson/documentation.html?highlight=subdomain_data