With the plastic casing off, we're able to peel that long antenna from the battery.
Finding the antenna here explains a bit about the AirPods' design. That hanging boom is for more than just balance—it's also to improve reception.
Digging deeper under more glued-on cables and tape, we find some markings etched into the battery. Looks like this is a 93 milliwatt hour battery—equivalent to a little over 1% of the charge capacity in an iPhone 7.