WebXR Api allows us to render 3D scenes to a AR/VR supporting device, like VR headset or any mobile device.
For devices which don't support WebXR Api yet, a polyfill is also available.
This example code shows how easy it would be to develop WebXR app and considering the fact that the online app already uses WebGL, most of the work is already done.
We can have a button in toolbar, clicking which it opens a VR (immersive-vr) scene. POC may include screen tap to move forward using XRInputSource/targetRayMode or use a controller. (If controller is not physically available, Google Carboard app allows emulation of controller using another phone via bluetooth).
With all these, adding AR/VR support becomes significantly easy.
I would have created a POC for this myself, but my unfamiliarity with the code base and the technologies involved make it really difficult for me to contribute in code.
I would request the devs or anyone who has familiarity with this codebase & JS to take this, as I'm sure it won't take more than a week to build a working POC for such an amazing feature.
I've worked on this separate from SweetHome3D, but I think it should be possible to have something similar in SweetHome3DJS: https://github.com/bobvanderlinden/sweethomewebxr/
It works with an exported OBJ file.
You can see the result here: https://bobvanderlinden.github.io/sweethomewebxr/