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. :
GameStop pulse 3D refurb $39.99! : r/PS5
Official wireless surround sound headset for PS3 released by Sony, includes 7.1 surround, mic, and its $99 (self.PS3) : r/PS3
Amazon.com: Black Shark Gaming Headset, Open Acoustic Gaming Headphones for PC, PS4, PS5, Xbox, Switch, 295G Ultra-Lightweight Headset with Microphone, Noise-Canceling Cardioid Mic, Stereo Surround 50mm Drivers : Video Games
Trade In Universal Afterglow Wireless Headset | GameStop
Amazon.com: Wireless Stereo Headset - Playstation 3 : Electronics
Amazon.com: PDP LVL30 Wired Headset with Single-Sided One Ear Headphone for PlayStation, PS4, PS5 - Mac, Tablet Compatible - Noise-Cancelling Mic - Lightweight, Cool Comfort, Great for Gaming - Black : Everything Else
Mortal Kombat - PlayStation 3 | PlayStation 3 | GameStop