What is a good Bluetooth headphone but also with a cable function for listening to music and playing Xbox?

I'm looking for headphones with the following functions:

Bluetooth
but also cable connection
to use for listening to music on the mobile phone
but also for use with Xbox one
over the ear
possibly noise canceling
if possible from a brand manufacturer
if it goes less than 100 euro

This is a present for a teenager.

I recommend headphones from JBL. SUPER sound quality. There are 60 euro

https://www.sony.de/electronics/kopfband-kopfhoerer/wh-ch700n

I use it - but not for gaming. It is currently available for less than 100 euro.