>  A Rust enum isn't even "quite close" to a C enum

This is incorrect. The following Rust enum compiles down to a single byte, whose variants are represented by the numbers 0, 1, and 2:

  enum Foo {
      Zero,
      One,
      Two
  }

You can even give them all numeric values explicitly:

  enum Bar {
      Ten = 10,
      Eighty = 80,
      TwoHundred = 200
  }

And you can also just tell it where to start and let it count from there:

  enum Qux {
      Five = 5,
      Six,
      Seven
  }

If you throw the #[repr(C)] attribute on any of these then Rust will make sure to size them as C would on your particular platform (on my machine this attribute inflates them from 8 bits to 64 bits), making them usable directly from C as well.