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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Sony Gold Wireless Stereo Headset for PlayStation 4 and PlayStation 3 Black 10029 - Best Buy
Sony's PS4 Headphone Surround Sound Tax | by Alex Rowe | Medium
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Will Your PS3 Headset Work with PS4? That's Not Easy to Answer | Push Square
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PS4: Current-gen headsets not compatible
The PlayStation Gold Headset is a really good one for PS3, they also work on PS4,5. They're kind of hard to come by nowadays though. : r/PS3
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How to Connect Bluetooth Headphones to a PS4
Gold Wireless Stereo Headset for PS4, PS3 & PSVita Hands On - YouTube
PlayStation 3 wireless headsets WILL work with PS4 - Tech Digest
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