Apple Battery Case serial number

I received a replacement Smart Battery Case for my iPhone XR. I had the serial number of the defective one from the original Apple Store receipt. However, the instructions with the replacement case is to keep the new serial number available in case of a failure within the 90 warranty for the replacement.

Where do I get the serial number? I don't have a purchase receipt and I can't find a way on the iPhone to show it. It is not in Settings -> General -> About like Airpods are.