3D WebView for Android with Gecko Engine is currently the only 3D WebView package that supports the Vulkan graphics API. However, I have a feature request to support Vulkan on Windows, and I will update this article in the future if I add support for that.
Vulkan requirements for Android
Requires 3D WebView v3.17 or newer.
Target devices must support the Vulkan extension VK_ANDROID_external_memory_android_hardware_buffer, which is supported on newer devices like Oculus Quest but isn't supported on all Android phones that support Vulkan. So, Vulkan is great to use if you're targeting a specific device like an XR headset, but it's not recommended if you're building an app for general Android phones, because some phones don't support the required extension.
Unity 2020.2 or newer is required for Vulkan. This is because Unity added support for using Texture2D.CreateExternalTexture() with Vulkan in 2020.2.
Android 8.0 (API level 26) or newer is required for Vulkan.