Ok, in a very, very rare case (so far never happened to me) when I really need to await an async operation in the destructor, I just define an additional async destructor, call it explicitly and await it. Maybe it's not very elegant but gets the job done and is quite readable as well.
And this would be basically what you have to do in Go anyways - you need to explicitly use defer if you want code to run on destruction, with the caveat that in Go nothing stops you from forgetting to call it, when in Rust I can at least have a deterministic guard that would panic if I forget to call the explicit destructor before the object getting out of scope.
BTW async drop is being worked on in Rust, so in the future this minor annoyance will be gone