Web-based VR content and 360˚ videos require a browser capability called WebXR. 3D WebView doesn't yet support WebXR, but I'm tracking a feature request for that and will update this page when I add support for WebXR in the future. If you would like to be added to the waitlist for WebXR support, please contact me and indicate what platform you're targeting.
For 3D WebView for Android with Gecko Engine, the underlying Mozilla GeckoView library has a low-level C++ API for passing VR headset data (like head pose and position) to the browser engine, but the amount of work needed to set WebXR up correctly is very significant. If you're interested in implementing that plumbing in your application, please download and read these technical notes about GeckoView's support for WebXR.