I am not sure that I understand exactly what you want, but in case it helps, my FQZ plugin is using the 3D webgl aspect of C3 to make quads that could be used as 3D billboard textures.
It has a mode where you can specify the x,y,z of each vertex of a quad. You could then use glmatrix.js and C3 scripting to do matrix math and set the position of the quad. I have included a mode where you can pull out the current camera P and MV matrices also if needed. Or you can just control the camera directly using camera location and look at.
Here's an example of it in use (this is with just billboard textures rotated to player view, etc.)
youtu.be/a-vo5fYRXvo
I am over on the Construct Community Discord, DM me there and I'll give you a key to try it if you want.
I don't know of another way to use C3 w/ 3D except for using Z elevation with sprites.
In your example youtube video, I think most (all?) of that could be done with almost vanilla C3. However it sounds like that still is not what you want?
Here's an example:
alcex.itch.io/psuedo-3d-racer-in-construct-3
Another example of matrix math w/ my plugin is this project (matrix math done in events, etc.):
mitsu-studios.itch.io/3djs