After applying the Geo-Node Modifier, you should use the function "merge by distance" to be sure there are no overlapping vertices (or use the Node "merge by Distance" inside the Node Tree) It is already integrated, but sometimes you have to make some "smooth" operation like "subdivide" or "smooth" the Objects.

Because the objects are created with maths formulas and they are not modelt, the face orientation in Blender could be "wrong", means the face orientation is not in the way you would like to have them. XYZ Axis can be shown in the negative way and cause this problem.

Like in my other setups the Material Slot has NO use until you aply the modifier. The Materials are configured with the "set material Node" in the Geometry Node Modifier and not with the material slot. If you work with new materials, you have to change in the "Material" Box in the Geometry Node Modifier!