It is succussed to save an empty group layer using following code in python window.
arcpy.management.SaveToLayerFile("Empty Group Layer", out_layer_path, None, "CURRENT")
However, in stand along script environment, the saved layer file is invalid. I changed the keyword "Empty Group Layer" to a layer object from .aprx file opened via arcpy.mp. (from aprx_map.listLayers()). Note: this empty group layer is manually generated in ArcGIS pro by right click MAP and click New Group Layer.
The documentation mentioned the input layer is a layer datatype that I assume this should work.