Typically, glTF/GLB files should not include the skybox in the file itself, at least not with the core spec. If you are using IBL for the sky, you can use this glTF extension to achieve it. I’m not aware of an extension that handles skyboxes the way you have it set up.
The Export to GLB button in the inspector automatically excludes certain types of skyboxes from the export already, but apparently it doesn’t cover SkyMaterial. Maybe we should add that to the exclusion code.