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. :
PlayStation Gold Wireless Stereo Headset 2.0 | Game Mania
Amazon.com: Playstation Gold Wireless Headset - The Last of Us Part II Limited Edition - Playstation 4 Accessory : Video Games