AirPods Max stop working when unplugged

I have the original AirPods Max headphones. When they are connected to a charger, the status light flashes and appears to behave normally. However, as soon as I unplug them from power, they stop working completely.

I am unable to pair them with any device, and I have also tried resetting them by holding the Noise Control button and Digital Crown, but the reset does not work. They are no longer covered by AppleCare.

Has anyone experienced this issue? Does this usually indicate a failed battery, charging component, or another hardware problem? Would it be worthwhile to have Apple inspect or repair them, or would replacement be the better option?