Vest Edge needs either a 3.5mm audio jack or a Bluetooth connection as its input. Headphones are usually connected via the Vest's audio output jack. However, when using PC USB headphones, you'll need to set up audio mirroring so that both the headphones and the Vest work simultaneously.
To apply audio mirroring you can use either Windows settings or external software. Please refer to this article for setting up audio mirroring on your PC, using VoiceMeeter free software.