Somebody just last year finally worked out what that battery is doing and why the adapter doesn’t work after it dies: https://www.projectgus.com/2023/04/griffin-imate/#mystery-ba... (discussed on HN: https://news.ycombinator.com/item?id=35772131)

(TLDR: compatibility with Apple’s off-USB-spec keyboard power button, but the circuit they used accidentally injects noise which wreaks havoc on the data lines when it’s unpowered and left floating.)