> You don't need mutex in async code, since there is no parallel execution whatsoever. In fact languages that use async programming as a first class citizen (JavaScript) don't even have a construct to do them.

This isn't even remotely true; plenty of languages have both async and concurrency, probably more than ones that don't. C# was the language that originated async/await, not JavaScript, and it certainly has concurrency, as do Swift, Python. Rust, and many more. You're conflating two independent proprieties of JavaScript as language and incorrectly inferring a link between them that doesn't actually exist.