Does the xbox series have a connection for headphones / headset or do I have to have a wireless connection or plug it into the controller
No, the Xbox has no audio output.
Who needs that too?
So already on the controller
The Xbox Series S itself has no audio output or input, since everything is now solved via HDMI, which can also transmit audio.
Wireless headsets are not required! You can also plug your headset / headphones into the controller without any problems. And don't worry about your audio connection! Compared to other controllers with Bluetooth, Xbox wireless technology gives you a significantly higher bandwidth and thus significantly better audio and voice quality.