Please do remember that Async programming is only beneficial to optimize the idle time of your threads away. For tasks where you already near 100% utilize your threads (e.g. computation heavy algorithms) something like async will not help you and will in fact make your codebase a lot more complex and difficult to reason about.
Should you have computation-heavy algorithms which you want to parallelize you can achieve that by making use of threading alone. A crate such as https://docs.rs/rayon/latest/rayon/ might help you a lot with this as well.