It definitely took me a couple of weeks to even start understanding what is happening but after that I don't think I can daily drive anything else lol

I've heard cachy is good, especially for gaming because of the kernel mods. I'm using NixOS, which definitely isn't recommended for anyone who's not a developer, but the package repository is massive. Almost any software that has been packaged anywhere is probably already in the repo.

Which distro did you pick?

You should add incoming and outgoing edges outside of the n-gon to the simulation. Right now, as far as I know, you don't use the fact that the edge path ends must be parallel to the original edges.

Your triangle tessellation can be generalized.

That would probably make the solution very asymmetrical. At least for cases where n is even a much simpler and symmetrical solution could perhaps be made (edge loops going straight across the n-gon to the other side).

Does the final algorithm have to be generalized for tessellation of arbitrary n-gons? What would happen if the bevel is applied to an intersection of, for example, 5 edges meeting at a vertex?