On ear / over ear Bluetooth headphones for music and gaming?

I would like to buy some reasonable on or over ear headphones (for listening to music) which I can also use for gaming (with aux cable on my Xbox) (the headphones must also have a microphone).

Would be optimal if the whole could stay below 100 euro.

Does jmd villt have a tip which headphones could be there?

Here I would go for the Audio-Technica ATH-M40x if it should stay below 100 euro, the ATH-M50x would be more expensive and better, otherwise models from Beyerdynamic or Sennheiser would be recommended.

If you want to go over it a bit, I recommend the beyerdynamic dt990 pro