I have now bought the Sony WH-1000 XM4 headphones and now wanted to connect them to the laptop, but on the laptop the headphones are only displayed as additional devices and not as a headset / headphones. I also don't hear "Bluetooth connected" on the headphones although the laptop says they are paired.
Look here.
https://helpguide.sony.net/mdr/wh1000xm3/v1/de/contents/TP0001703215.html
Send the scrap back and buy you good headphones, I would say.
And what do you think are "good" headphones?
Your laptop may be broken
Why scrap?
Because cheap technology with an equalizer in a plastic housing is?
I could recommend the Technics EAH-F50B to you. Clear, high-resolution sound, crisp bass and not as distorted as from the overpriced Sony part.
That is high end technology. And the best headphones are all made of plastic