How do the view-dependent effects get "discovered" from only a single source camera angle?
Actually there are multiple source cameras. The neural net learns to interpolate the source camera colors based on where the virtual camera is. Under the hood it's hard to say exactly what's going on in the mind of the neural net, but I think it's something like "If I'm closer to camera A, take most of the color from camera A."
Gaussian splatting does not use neural nets. It runs an optimizer on the Gaussian splattering parameters. I think in your comment you are talking about Neural Radiance Fields (Nerfs).
Traditionally you'd use an optimizer, but OP isn't doing it traditionally, which is what makes it interesting. NeRFs work differently.