Why is the smart battery case not working?

I’m assuming you purchased the iPhone 8 second hand? That phone should support an accessory like that however there may be some caveats. There’s a USB validator chip known as TriStar or Hydra depending on the model (I believe Hydra is in the X and above). Anyways these chips check to make sure that whatever you plug into the lightning port is safe to use and won’t cause harm to the device by talking to another circuit chip located in the device you connected. A good quality accessory will have surge protection built in to ensure no harm is done if something goes wrong. However, cheaper accessories will “trick” TriStar and cause harm. If you purchased that iPhone 8 second hand there could be a possibility that it had some underlying issue.