The PlayStation Gold headset is probably the only wireless headset which is directly compatible with PS3, PS4, PS5, Android, PC, Switch (Personally tested) Get hold of them before they are super rare. :
Amazon.com: XP300 Xbox 360 & PS3 Headset- CAN/EU : Video Games
Amazon.com: Turtle Beach - Ear Force P11 - Amplified Stereo Gaming Headset - PS3 - FFP : Video Games