Great video!

If you'd be interested, I think a video on the Walk on Spheres method for this problem could be valuable. WoS is an old and mostly overlooked Monte Carlo integration method, but it has received some interest recently due to a 2020 paper that refined it and extended it to other PDEs.

Here's a real-time 3D ShaderToy example with a neat double-torus boundary: https://www.shadertoy.com/view/wdffWj

and a quick and dirty implementation in Python:

https://gist.github.com/GregTJ/6f3b86e7ef6a2e776174026ceae369ad