AR frameworks generally have some basic device capability requirements to support the tracking, rendering etc. Beyond the obvious requirement for a camera, or some sort of video input, there is often the use of orientation sensors etc.
For example, Google says the following about certifying devices for ARCore support (at this time):
Certification is important because we want users to have a good experience with your AR application. This is primarily related to sensitive motion tracking, which is done by combining the camera image and the motion sensor input to determine how the user's device moves through the real world.
I am sure you are aware of this, but its worth mentioning in case there is any misunderstanding that a Web API would allow AR to work seamlessly across laptops, or lower end mobile devices etc.
VR, on the other hand, does not usually have as stringent requirements and there has been for a while an initiative to provide a Web VR framework - WebVR:
This has now evolved into WebXR, which is intended to cover both VR and AR, although the same caveats on device capabilities will still apply:
WebXR is new and evolving so finding support may be tricky - there are some examples here: https://immersive-web.github.io/webxr-samples/, but you may find you see this message more often than not:

At this time, for example, the latest version of Safari on latest version of OSX does not support it but Chrome on OSX will support.
If you are primarily interested in mobile devices, then React Native may be worth looking at - for example iOS ARKit support is available in this open library:
There is also a web triggered device specific support for Android viewing of AR models, although I suspect this is not what you are looking for:
One of the most interesting development and evolving areas in AR is 'Occlusion' - how one object may be in front or behind another real or AR object.
There is quite a bit of focus on this at the moment, both in SW and HW approaches. If the most popular, or powerful, solutions that emerge rely on some sort of device HW depth sensor in the future this may again restrict certain functionality to certain device types.