rustdoc silently fails parsing some doctests when using a playground URL

[ollie27]

For example running rustdoc --markdown-playground-url=https://play.rust-lang.org/ foo.md on:

# test

```
# #![feature(async_await)]
use std::future::Future;
use std::pin::Pin;
fn foo_recursive(n: usize) -> Pin<Box<dyn Future<Output = ()>>> {
    Box::pin(async move {
        if n > 0 {
            foo_recursive(n - 1).await;
        }
    })
}
```

results in a 0 byte file and no error messages but a none zero exit code. It should succeed. This has the same root cause as #59313 and #59557 but it only occurs when using a playground URL.