taby said:
OK, one big problem: my code does not specify a light source, not even once.

In naive path tracing that's not generally a big problem (as was mentioned - that doesn't require lights definition at all - only material emissivity), but … the moment you start doing improvements for better convergence (explicit sampling - also known as next event estimation … being the most common), you NEED to know your lights. The big question is - what are the lights? And that boils down to how you define your scene.

• Using just geometry with emissive lights is fine, you can create a buffer with triangle indices that are emissive and use those (I used this approach in my BSc. and MSc. theses).
• Lights can also be defined separately (even with no geometry associated), then you need a separate buffer for those and ensure that the lightning behaves properly
• Lights can also be defined only based on environment map (i.e. image based lightning - F.e. through skydome or skybox) - then some way of sampling the environment (i.e. skydome/skybox) is needed

Main difference between naive path tracing and explicit one is that explicit one takes just few samples per pixel to produce already quite smooth image:

With some improvements - explicit path tracing can therefore produce almost smooth images within just few samples per pixel (thus you can achieve real time path tracing). Especially for scenes with mainly diffuse surfaces. They do require knowledge about lights though (as they have to explicitly sample them). The terms “explicit path tracing” or “next event estimation in path tracing” are a bit confusing, but in general interchangeable.

taby said:
So, even though I have caustics working

Caustics will work in path tracers by default - the problem is, the caustics work properly and are visible in your test because your light is large enough and you can do ridiculous amount of samples. If you look at smallpt (url: https://www.kevinbeason.com/smallpt/​),​ that's a very nice reference path tracer. You can clearly see caustics working there too.

The main problem is convergence rate for caustics - for naive path tracing, or even explicit one - it is quite low. You have to throw thousands and thousands of samples to get it properly for larger lights, and many more (in order of magnitudes) when your light is small.

There are extensions - like bi-directional path tracing - that help convergence a bit, at cost of algorithm complexity.

Okay - let me demonstrate. I ran 2 variants (one with naive path tracing, one with explicit (next event estimation) path tracing). Next image is large (beware) - sorry for posting this monstrosity:

So… you should be able to clearly see impact of 2 things. Explicit sampling vs. light size, and caustics noise vs. light size. The bigger the light, the better the caustics - using naive vs. explicit has a major impact on the scene, but not really that big on quality of caustics (unless light is too small!). The only way how you could get better convergence for caustics would be using bi-directional path tracing (and I'd dare to say metropolis light transport would be better than monte carlo approach, especially for caustics - but that's from experience).

I sadly don't have any equivalent/similar implementations of path tracers that can be easily changed like smallpt in shadertoy, that implement bi-directional with neither metropolis light transport nor monte carlo. So I can't quickly provide comparison to those.