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. :
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Amazon.com: Gold Wireless Stereo Headset - PlayStation 4 : Video Games
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Gadget Review: PS3 Pulse Wireless Stereo Headset
Sony Pulse Review | Elite Edition (PS3) | Wireless Headset | Digital Trends
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PS4 system update 1.60 to add Pulse headset support tonight - Gematsu