how to connect xbox series S to studio display?

one quick search on youtube: apple studio display xbox

you need Elgato HD60X

https://www.youtube.com/watch?v=xz4ACrXBWqs

and here

https://www.youtube.com/watch?v=-OHU9Ml03UE

but honestly the Studio Display sucks a lot for gaming....for me it sucks for all my demands and i will send it back to Apple. Bad unnatural "bass-effective" sound and the Display for me does not fit for the Price over 1500 Euros. Maybe its good for creatives, but not for casual Users. But my new mini m2 pro is great. Guess i go for 2 27 IPS at 1080p native. I come from a 2011 iMac and what should i say, i prefer the picture of the 2011 over the Studiodisplay.

XBOX/PS is build for OLED :-)

You can use "OneCast" to stream from Xbox to your Mac.

Not possible unfortunately.