Yeah, I ran into the exact same problem. If anyone is wondering why this happens, it's a bug in the game engine itself, which struggles with audio capture when wireless devices are involved. The game picks up your voice signal, but the engine freezes up and fails to save or output the recorded audio file if Bluetooth headphones are set as the default device.
To fix it, you can set your standard motherboard audio and your microphone as the default devices in Windows, and then plug in regular 3.5mm wired headphones directly into the back of your PC. If you really want to use wireless headphones, you'll need to install a virtual audio cable program to bridge the audio stream so the game thinks it's working with a standard wired connection, and then everything will record and playback properly.
