Rollup merge of #125259 - compiler-errors:fn-mut-as-a-treat, r=oli-obk

An async closure may implement `FnMut`/`Fn` if it has no self-borrows

There's no reason that async closures may not implement `FnMut` or `Fn` if they don't actually borrow anything with the closure's env lifetime. Specifically, #123660 made it so that we don't always need to borrow captures from the closure's env.

See the doc comment on `should_reborrow_from_env_of_parent_coroutine_closure`:

https://github.com/rust-lang/rust/blob/c00957a3e269219413041a4e3565f33b1f9d0779/compiler/rustc_hir_typeck/src/upvar.rs#L1777-L1823

If there are no such borrows, then we are free to implement `FnMut` and `Fn` as permitted by our closure's inferred `ClosureKind`.

As far as I can tell, this change makes `async || {}` work in precisely the set of places they used to work before #120361.
Fixes #125247.

r? oli-obk

Author: fmease