[Demangle][Rust] Hide implementation details NFC

Move content of the "public" header into the implementation file.

This also renames two enumerations that were previously used through
`rust_demangle::` scope, to avoid breaking a build bot with older
version of GCC that rejects uses of enumerator through `E::A` if there
is a variable with the same name as enumeration `E` in the scope.

Reviewed By: dblaikie

Differential Revision: https://reviews.llvm.org/D104362