Light passing by the Schwarzschild black hole [video]

Good question. Without seeing the code that produced this, I'm stuck making some educated guesses.

The "splitting" effect is forced by the enormous computational expense of the numerical relativity calculations.

Instead of thinking of the initial yellow pulse as a plane wave, think of the animation as tracing-out the evolution of a number of representative initial positions in that plane wave. We don't see the full density of the many-many-many particle pulse in any frame. (We're also only seeing two spatial dimensions). We just see pixels lit depending on where the initial positions have led to.

We don't really see advancing "beams" as such, it's just that pixels are left lit even after they spatial positions they represent have emptied. The dimming of previously-lit pixels is artistic license.

The youtube video also doesn't show us the light's change in energy-momentum ("frequency", equivalently), although the twitter version in my other comment (or here: <https://twitter.com/PeRossello/status/1756697785083023812>) does, with the caveat in the second tweet in the thread. (The thread has some nice goodies in it for experts).