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. :
Amazon.com: Defean Replacement Headband Cushion Compatible with Sony PS3 PS4 Wireless Stereo Headset CECHYA-0080 Headphones : Video Games
PS4: Current-gen headsets not compatible
PlayStation 3 wireless headsets WILL work with PS4 - Tech Digest
Gaming Headset for PS4, PS5, Xbox One, Nintendo Switch, EEEkit, Stereo Gaming Headphones with Noise Canceling Mic, Memory Earmuffs, LED Lights, 3.5mm Over-Ear Headphones for PC, PS3, Mac, Laptop - Walmart.com
Sony Playstation Wireless Stereo Headset 2.0 for PlayStation 3, PlayStation Vita, PlayStation 4
PS3 Wireless Headset Repair - iFixit
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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Buy Ps3 Headset Work On Ps4 | UP TO 57% OFF
Gold Wireless Stereo Headset for PS4, PS3 & PSVita Hands On - YouTube
Sony PlayStation Wireless Stereo Headset 2.0, PS3/PS4
Gaming Headset with Mic for PS4, PS5, PC, Xbox One, EEEkit Surround Sound Noise Cancelling Over Ear Headphones with Soft Memory Ear Pads Compatible with Laptop Tablet Mobile Phone Computer - Walmart.com
Sony Pulse Wireless Stereo Headset Elite for the PS3 - Sam's Club
Sony Rolling Out New Gold Wireless Headset This Month | Push Square
Amazon.com: Replacement Black Cushion Ear Pads Earmuff earpads Cup Cover Pillow Compatible with Sony ps3 ps4 Gold Wireless CECHYA-0083 Stereo 7.1 Virtual Surround Headphone Headset : Video Games