Using stuff like this, does it make sense to use Rust in a golang-style where instead of async and its function colouring, you spawn coroutines and synchronize over channels?
It doesn't matter if you use channels or mutexes to communicate between tasks, you still need your function to be async to spawn it as a coroutine. Your only choice is between coroutines (async tasks spawned on an executor) or regular OS threads. Channels work with both, the rule of thumb is to use async when your workload is IO-bound, and threads when it is compute-bound. Then, it's up to you whether you communicate by sharing memory or share memory by communicating.
If you are more like "parallel" than "async" totally yes!
here "parallel" is used in the most broad sense where you have (probably unrelated) tasks that are mostly independent for each other and run to completion. In that case "async" is an anti-pattern. So if you work more process-based that switch-based go!