How to have a keymap work in object mode and edit mode? [duplicate]

Question

I've created an operator that uses a keymap to activate it. While it works in object mode, it is not being called in edit mode. Is there a way to get this to run in edit mode too?

import bpy


class GridRescale(bpy.types.Operator):
    """Change grid scale"""
    bl_idname = "kitfox.grid_rescale"
    bl_label = "Grid Rescale"
    bl_options = {'REGISTER'}

    def invoke(self, context, event):
        scale = bpy.context.space_data.overlay.grid_scale
        
        if event.type == "LEFT_ARROW":
            scale /= 2
        elif  event.type == "RIGHT_ARROW":
            scale *= 2
        
        bpy.context.space_data.overlay.grid_scale = scale
        self.report({'INFO'}, "Grid scale: %f" % (scale))
        return {'FINISHED'}


# store keymaps here to access after registration
addon_keymaps = []


def register():
    bpy.utils.register_class(GridRescale)

    # handle the keymap
    wm = bpy.context.window_manager
    km = wm.keyconfigs.addon.keymaps.new(name='Object Mode', space_type='EMPTY')

    kmi = km.keymap_items.new(GridRescale.bl_idname, 'LEFT_ARROW', 'PRESS', ctrl=True, shift=False)
    kmi = km.keymap_items.new(GridRescale.bl_idname, 'RIGHT_ARROW', 'PRESS', ctrl=True, shift=False)

    addon_keymaps.append(km)
    
    

def unregister():
    bpy.utils.unregister_class(GridRescale)

    # handle the keymap
    wm = bpy.context.window_manager
    for km in addon_keymaps:
        wm.keyconfigs.addon.keymaps.remove(km)
    # clear the list
    del addon_keymaps[:]


if __name__ == "__main__":
    register()