I think this is a clash of terminology: a Rust enum isn't an integer with pretensions of an identity.

You'd describe it as a tagged union in some languages. So when you say you'd return an error with extra information, what that information is is associated with the specific variant of the enum.

Using yuriks AllocError as an example, if the error is SizeTooLarge, it has the size field. Other errors may have no additional data, others may have different data.

When you return an error from your allocating function, it's a known size, the size of the largest enum variant + the discriminant (tag).