Rename operation does not rename examples in docstrings

Given cargo new --lib rename with contents:

/// Prints "Hello, world!".
///
/// # Example
/// ```rust
/// use rename::hello;
/// hello();
/// ```
pub fn hello() {
    println!("Hello, world!");
}

and using the rename operation (F2 in VSCode) on the hello() function, you end up with

/// Prints "Hello, world!".
///
/// # Example
/// ```rust
/// use rename::hello;
/// hello();
/// ```
pub fn hello_world() {
    println!("Hello, world!");
}

which results in cargo test breaking:

---- src/lib.rs - hello_world (line 4) stdout ----
error[E0432]: unresolved import `rename::hello`
 --> src/lib.rs:5:5
  |
4 | use rename::hello;
  |     ^^^^^^^^^^^^^ no `hello` in the root

error: aborting due to previous error

Considering rust-analyzer manages to provide syntax highlighting within the docstring example blocks, it would be nice if the rename operation affected the docstrings as well.

Reproduce the issue with the shown cargo new --lib rename example and the VSCode F2 rename operation, then run cargo test to confirm the doctest failure. Trace how rename handles symbols in Rust docstring example blocks; done means the renamed function and its references in the example stay consistent and cargo test passes.