How can I see an iPhone Smart Battery Case serial number using macOS console?

1. Put your iPhone into the Smart Battery Case.
2. Unlock your iPhone.
3. Open Console.app on macOS.
4. Plug your Lightning cable into your computer.
5. Plug in the other end of the Lightning cable into your iPhone via the Smart Battery Case Lightning port.
6. Your unlocked iPhone may ask if you trust this computer. Select Trust and enter your iPhone passcode.
7. In Console.app, select your iPhone on the sidebar.
8. Type Accessory Identifier into the Console.app search bar.
9. In the Console.app window, you will see a number of items under process sharingd with text in the message containing In powersource description.
10. Select one of these items and look for the line "Battery Case", "Accessory Identifier" :. The serial number for the Smart Battery Case will be listed there.

This is not using the Console.app, but if you just want the serial number, the easiest thing to do is navigate to Settings > Privacy > Analytics > Start Diagnostics.