Not recognising my Logitech headset?

I’m using Windows 10 and Audacity

For some reason, Audacity isn’t recognising my Logitech USB headset for playback or recording, despite the headset working for every other program on my computer as far as I’m aware.
Under the “Devices” part of the Preferences, the only option for playback is “Speakers/Headphones (IDT High Definition Audio Codec)” which I’m assuming must just be my regular speakers, since I get playback just fine through them. Under the recording section it has the same again, plus the microphone from my Microsoft LifeCam webcam, but not my headset.
When I have my headset plugged in, Audacity just keeps playing the sound through my main speakers while the rest of my computer’s audio goes through my headset. I can’t work out what’s going wrong here, could it be a driver issue or something?

Ensure that you connect the headset before launching Audacity.
If you connect the headset after Audacity is started, you have to tell Audacity to re-scan for audio devices so that Audacity knows about the headset (Transport menu > Rescan audio devices).