Incorrect rejection of async code on type not living long enough

Compiling the following code:

trait Foo: Sync + Send {
    type A<'a>: Bar + 'a
    where
        Self: 'a;

    fn get<'a>(&'a self) -> Self::A<'a>;
}

trait Bar: Sync + Send {}

fn do_something<'a, T: Foo + 'a>(obj: &'a T) -> impl Future<Output = ()> + Send + 'a {
    async move {
        let x = obj.get();
        tokio::time::sleep(std::time::Duration::from_secs(1)).await;
        drop(x)
    }
}

I would have expected it to compile without errors. Instead it reports

   Compiling playground v0.0.1 (/playground)
error: `T` does not live long enough
  --> src/lib.rs:12:5
   |
12 | /     async move {
13 | |         let x = obj.get();
14 | |         tokio::time::sleep(std::time::Duration::from_secs(1)).await;
15 | |         drop(x)
16 | |     }
   | |_____^

error: could not compile `playground` (lib) due to 1 previous error

Removing either the Send bound on the future returned by do_something, or removing the sleep call, both make the function compile succesfully.

Should anyone else run into this, the following workaround is accepted as by the compiler:

trait Foo: Sync + Send {
    type A<'a>: Bar + 'a
    where
        Self: 'a;

    fn get<'a>(&'a self) -> Self::A<'a>;
}

trait Bar: Sync + Send {}

fn do_something<'a, T: Foo + 'a>(obj: &'a T) -> impl Future<Output = ()> + Send + 'a {
    fn do_inner<'b, U: Bar + 'b>(x: U) -> impl Future<Output = ()> + Send + 'b {
        async move {
            tokio::time::sleep(std::time::Duration::from_secs(1)).await;
            drop(x)
        }
    }
    async move {
        let x = obj.get();
        do_inner(x).await
    }
}

This may be related to #92096, but the code and error are different enough that I am not entirely sure about that.

Meta

This occured on a nightly compiler version from rust playground, and on the latest stable (1.88.0). Rust playground reported the following version info for nightly:

(2025-07-03 da58c051315268a197ce)

Start by reproducing the example in Rust Playground on stable 1.88.0 and nightly 2025-07-03, then compare it with the variants that remove the Send bound or sleep call. Read the related discussion in #92096 and determine whether the reported lifetime rejection is expected. Done means the original example compiles correctly and the behavior has regression coverage.