Do not use Ps4 controller and USB headset at the same time?

My keyboard and my headset connected to my PC. If I want to connect my PS4 controller, can't I use my headset anymore? Does anyone know why this is? Both work

Simply switch the sound output to the headset after plugging in the controller.

USB Headset is so called a headset with integrated sound card that only works on either Windows or maybe even Mac or Linux.

It's the same as trying to connect my USB sound card to Playstation and I'm wondering why that does not work.

Connect the headset to the controller!