Why Rust chose to use an enum for the Option type instead of a trait?

In Rust, we have the Option type defined as:

pub enum Option<T> {
  None,
  Some(T),
}

Just wondering from a programming language implementation/theory standpoint (using Rust as inspiration), why this was defined as an enum and not something else, such as using traits.

pub struct None {}

pub struct Some<T> {
  value: T
}

pub trait Option<T> {}

impl Option<T> for Some<T> {}

impl Option<T> for None {}

I don't know if something like this would really work, but something along these lines.

P.S. I don't have a deep practical understanding of Rust yet, just learning it's APIs and reading the docs to get a better understanding of type systems.