With the board removed, we're able to extract the full battery cable assembly—with plenty of odds and ends attached to it:

The gesture control cable

Two connectors, one for the board and one for the driver assembly

An antenna cable

Goodix GH611 in-ear detection chip/touch controller

The soldered battery which is running at 3.7 V with 31 mAh. This sums up to ~0.11 Wh. For those interested, the button cell has a ~10 mm diameter and a height of ~4.4 mm.