Rendering an equirectangular 360-degree 3d-stereoscopic view of a scene is tricky because the offset from the origin of the cameras needs to change for every vertical pixel on the screen.
As explained very well in this amazing page by shubhmehta, if you are not careful what you'll get is a view from two eyes swiveling in their sockets:
when what we need is a map from a head rotating two eye-cams:
We create two pairs of cameras, point one 45 degrees to the sky and one 45 degrees to the floor, then rotate them around like doing a panorama shot with your phone.
Which means you'll need to pause your game while you take a panoramic photograph or you'll get similar duplicated people and elongated dogs etc.
It's going to take quite a few frames.
We reduce the number by having more than one camera. You can set what number you want. I found after about 60 adding more cameras became less useful as it slowed down the each-frame render so much that doing fewer-frames wasn't helpful.
That gives us a perspective projection, and the VR headsets all want an equirectangular projection, so we do a final pass over the image when it's complete to warp it to make it equirectangular.
You may want to create a background panorama of your scene for environment mapping, or just want to make a whole-world screenshot someone can see in VR, or you might want to stitch thousands of them together to make a VR movie. That's why I needed it.
Licence is CC0, do whatever you want.
All you really need is PanoRenderer.cs which you can attach to a Node3D in your scene.
When your code wants to start a render, move that Node3d to the view-point, and call the StartRender function of the PanoRenderer.
Then call isFinished() each frame to see if it's finished.
The other files here are a demo scene if you want to check it out in it's own project first.