Ever since https://github.com/rust-lang/rust/pull/34828 you can transform any `f` that takes a `T` into an `f` that takes an `Option<T>` without any of the call sites changing.
For instance, look at this playground https://play.rust-lang.org/?version=stable&mode=debug&editio...
Your function `get_string_raw` which just handles `i32` can be transformed into a function `get_string` which handles `Option<i32>` without the thing calling changing how it calls the function. And the new `get_string` can accept `Some(i32)` or `None` or just `i32`.
Of course, this is slightly broad for brevity: you can now pass in anything that can become an `Option<i32>` but you can just define a trait to restrict that if you wanted.
You can get that sort of covariant effort that you wanted.