The Quest 2 is a wireless headset, but you officially need to plug it into your gaming PC via a USB Type-C cable to enjoy the best VR headset experience with your rig. But there are now easily accessible ways to do that wirelessly. However, you do need to have a Wi-Fi 6 router to deliver the level of throughput you require not to spend the entire time vomiting your guts up due to incessant lag.
The old Vive did have a wireless module you could add to the system, which was almost effective, though, in our experience, the connection dropouts would not be something we could put up within the long term.
The Valve Index could be due to its own wireless module as some patents have emerged, indicating a wireless head strap has at least been considered for the company's stellar goggles.