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. :
PS3 Wired Chat Headset | Video Game Heaven
New Official Wireless Stereo Headset Coming for PS3 – PlayStation.Blog
Turtle Beach PS3 Ear Force PX21 Gaming Headset review: Turtle Beach PS3 Ear Force PX21 Gaming Headset - CNET
Official Bluetooth Headset for the PLAYSTATION 3 – PlayStation.Blog
Amazon.com: PS3 Bluetooth Headset : Video Games
Sony PlayStation 3 Pulse Elite Edition Wireless Headset [Brand New] | eBay