Installing GNU compilers on PureDarwin/Darwin?
Your link is broken to the instructions.

FYI, the point of macOS is, to a large degree, the fact that it IS a walled garden. Having control over the entire hardware and software stack lets Apple provide a seamless, polished service and products at a premium cost.

As far as Homebrew goes, as a maintainer, I have zero optimism that it will work at all, unless the Linux version can be coerced to get installed and/or run, then maybe it could work (no promises) but will likely require a lot of time compiling things. Normal Homebrew (on macOS) checks for Xcode CLT and other very macOS specific stuff that won't be present in Pure Darwin. I think Homebrew on Linux will also fail because it looks for Linux headers, etc.

No matter what, this is an unsupported configuration for Homebrew and I'm 99% sure it won't work, but would be curious to learn where it fails.

I would assume/guess PureDarwin has some sort of package manager, or a package manager planned? Maybe?