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: LETTON Gold Wireless Gaming Headset with Detachable Mic - Playstation (PS4, PS5) PC - Dynamic EQ Compensation Pro Audio, Noise Cancelling Microphone, Ultra-Comfort Over-Ear Headphones : Video Games
Ps4 Gold Limted Edition Uncharted Wireless Headset for Sale in Hillsboro, OR - OfferUp
Sony PlayStation Gold Wireless Headset Review | PCMag