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 Pulse Wireless Headset Review - YouTube
HEADSET WIRELESS BLUETOOTH COOLGEAR COOLCOM (PS3) - GCTECH
Onn Chat Headset For Playstation 3, Black, Ona13Mg511 - Walmart.com
Sony Wireless Stereo Headset 2.0 Ακουστικά Black - PS4 / PS3 / PS Vita
Sony Wired Stereo Headset 7.1 Virtual Surround (PS4/PS3/PSVita) | Skroutz.gr
DOBE gaming headset and mic compatible with PS5, PS4, PS3, 360, One, Switch and PC – TALENTEC
Review: PS3 headset gets high marks for sound quality | Ars Technica