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. :
PlayStation Gold Wireless Headset - Black [PlayStation 4 Accessory] - Walmart.com
PlayStation 4 Gold Wireless Headset Rose Gold | GameStop
Geekria QuickFit Protein Leather Replacement Ear Pads for Sony PlaySta
Amazon.com: Gold Wireless Stereo Headset - PlayStation 4 : Wireless Stereo Headset: Video Games