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.)

That's interesting. My iMate is flaky — I'll pop it open and check!