Power supply over USB cable
The first version of binaural head used batteries and charging circuit integrated inside the head. But strangely enough it was not as practical as it seems. By using USB power supply you can power the microphone from any USB port. Be it a phone charger or a laptop or a power bank. It is very flexible solution. If power bank gets empty you can easily change it or use any size of power bank. Sometimes too many integrations create more problems than benefits.
For sure USB power supply doesn't reduce quality by any means. The power circuit is completely galvanically isolated with two stage power filtering. For example, lithium-ion battery can have up to 5 uV RMS noise by itself. The microphone power circuit has less than 1 uV RMS noise over 20Hz - 20kHz bandwidth.