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. :
Razer Thresher for PS4 - Wireless and Wired Gaming Headset | Razer Europe
Sony PlayStation 4 Gold Wireless Headset Fortnite Neo Versa Bundle PS4 | eBay
Genuine Sony Wireless Stereo Gaming Headset 2.0 PlayStation 4 PS4 PS3 PS Vita | eBay
SONY PS4 Kiegészítő Wireless Stereo Headset 2.0 - bevachip.hu