Stealth 600 Gen 2 White Wireless Gaming Headset for Xbox One
Xbox Series X
Based on some articles that I have come across in my, more difficult than it should be, search for the perfect headset, once the headset is ready to connect or is in pairing mode, push the button that should be next to the power button on the Xbox One itself. That is the "sync" button you use most often for (re)-connecting controllers and certain, compatible headsets to the Xbox. Hope this helps!
Unfortunately, no you can't as this headset is designed specifically to connect directly to the Xbox One, X/S via Xbox Wireless, the wireless connection protocol used to connect controllers and headsets such as this one. This is not considered a Bluetooth headset, which is what you would need. Hope this helps!