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. :
PULSE 3D wireless headset | The official 3D audio headset for PS5 | PlayStation
The 24k Gold Partly PlayStation PS5™ console | Goldgenie
PlayStation Gold Wireless Headset review - SoundGuys
Amazon.com: PlayStation Gold Wireless Headset Rose Gold 4 : Video Games
PlayStation Gold Wireless Headset review - SoundGuys
Sony Playstation 5 Disc Version Console with Extra White Controller, White PULSE 3D Headset and Surge QuickType 2.0 Wireless PS5 Controller Keypad Bundle | Pro-Distributing
Don't Worry, Your PS4 Headphones Will Probably Work on PS5 | Push Square