Blender add-on for removing empty shape keys.

RemoveUnusedShapeKeys.py

bl_info = {
    "name": "Remove Unused Shape Keys",
    "blender": (2, 80, 0),
    "category": "Object",
}

import bpy
import numpy as np


class RemoveShapeKeys(bpy.types.Operator):
    """Removes unused shape keys on all selected objects owo"""      # Use this as a tooltip for menu items and buttons.
    bl_idname = "object.rm_shapekeys"        # Unique identifier for buttons and menu items to reference.
    bl_label = "Remove Unused Shape Keys"         # Display name in the interface.
    bl_options = {'REGISTER', 'UNDO'}  # Enable undo for the operator.

    def execute(self, context):        # execute() is called when running the operator.
        
        # Tolerance to small differences, change it if you want
        tolerance = 0.001

        assert bpy.context.mode == 'OBJECT', "Must be in object mode!"

        for ob in bpy.context.selected_objects:
            if ob.type != 'MESH': continue
            if not ob.data.shape_keys: continue
            if not ob.data.shape_keys.use_relative: continue

            kbs = ob.data.shape_keys.key_blocks
            nverts = len(ob.data.vertices)
            to_delete = []

            # Cache locs for rel keys since many keys have the same rel key
            cache = {}

            locs = np.empty(3*nverts, dtype=np.float32)

            for kb in kbs:
                if kb == kb.relative_key: continue

                kb.data.foreach_get("co", locs)

                if kb.relative_key.name not in cache:
                    rel_locs = np.empty(3*nverts, dtype=np.float32)
                    kb.relative_key.data.foreach_get("co", rel_locs)
                    cache[kb.relative_key.name] = rel_locs
                rel_locs = cache[kb.relative_key.name]

                locs -= rel_locs
                if (np.abs(locs) < tolerance).all():
                    to_delete.append(kb.name)

            for kb_name in to_delete:
                ob.shape_key_remove(ob.data.shape_keys.key_blocks[kb_name])

        return {'FINISHED'}            # Lets Blender know the operator finished successfully.

def menu_func(self, context):
    self.layout.operator(RemoveShapeKeys.bl_idname)

def register():
    bpy.utils.register_class(RemoveShapeKeys)
    bpy.types.VIEW3D_MT_object.append(menu_func)  # Adds the new operator to an existing menu.

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


# This allows you to run the script directly from Blender's Text editor
# to test the add-on without having to install it.
if __name__ == "__main__":
    register()

Just this bundled as an add-on.

To install, save this file somewehere, then in blender: Preferences -> Add-Ons -> Install... and select the file.