Your setup is good so far. What you need for the inner face is simply to join the original mesh before extrusion to the extruded one. Since the normals on the inside are facing in the wrong direction now, you need to also place a Flip Faces node after the Curve to Mesh before the Join Geometry node.
The problem with the Extrude Mesh node in GN is that there is no "Even Thickness" setting like in the Solidify modifier. So in some or more likely a lot of cases you will not get a similar result.