I think it's like CPython. The original implementation of the Python programming language was just called Python. Once there were multiple implementations it became useful to call it CPython sometimes. It depends on the context. Nix is both a language and an implementation. Calling the original implementation of Nix CppNix is a way to distinguish it from other implementations (like Tvix or Lix).

Edit: This is not a comment on the rest of the content of your post. I just thought it was kind of fair to call it CppNix!