Rollup merge of #123350 - compiler-errors:async-closure-by-move, r=oli-obk

Actually use the inferred `ClosureKind` from signature inference in coroutine-closures

A follow-up to https://github.com/rust-lang/rust/pull/123349, which fixes another subtle bug: We were not taking into account the async closure kind we infer during closure signature inference.

When I pass a closure directly to an arg like `fn(x: impl async FnOnce())`, that should have the side-effect of artificially restricting the kind of the async closure to `ClosureKind::FnOnce`. We weren't doing this -- that's a quick fix; however, it uncovers a second, more subtle bug with the way that `move`, async closures, and `FnOnce` interact.

Specifically, when we have an async closure like:
```
let x = Struct;
let c = infer_as_fnonce(async move || {
  println!("{x:?}");
}
```

The outer closure captures `x` by move, but the inner coroutine still immutably borrows `x` from the outer closure. Since we've forced the closure to by `async FnOnce()`, we can't actually *do* a self borrow, since the signature of `AsyncFnOnce::call_once` doesn't have a borrowed lifetime. This means that all `async move` closures that are constrained to `FnOnce` will fail borrowck.

We can fix that by detecting this case specifically, and making the *inner* async closure `move` as well. This is always beneficial to closure analysis, since if we have an `async FnOnce()` that's `move`, there's no reason to ever borrow anything, so `move` isn't artificially restrictive.

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