I mostly am pretty happy with this code. The major outstanding issue is some discontinuties in the normals; it's unclear if this is a correctness issue on my part or if the subdivision scheme is just not precise enough to get this right; there are a few more details below.
There are some performance issues on my machine (which is not the best, especially GPU wise), especially to do with compiling the shader. Just a warning to expect that to take a little while.
Slerping works, mostly. It's certainly better than without interpolation:
There is still some issue with discontinuities. Either my slerping is not accurate enough, or more subdivisions are needed. Here's a picture with a more extreme curve which demonstrates this:
It's totally possible there's a numerical error in my code somewhere. However, I think this could also be just an issue with the granularity of this subdivision scheme; similar discontinuities (in particular slight square-ish-ness of reflections of spheres) seem to exist in the example photo.
The mirror's shadow also works, though it's very binary, and so it doesn't look great:
There's an optional toggle for multibounce:
Here's no multibounce, for comparison:
This seems to work, mostly. The major issue is likely not with this code. Instead, the discontinuities from slerping (whether because of a numerical error in my code or insufficient subdivision depth) become significantly more noticeable when multibounce is enabled; presumably this is because the effect is cumulative.
Here's another one with multbounce, this time with much less subdivision; this is probably my favorite picture to come out of this: