JS does support concurrent execution, Promise.all is an example. Without it, JS async would make little sense. The problem very much exists there, and try-catch is only a surface-level answer. As you can see here [1], the interaction of cancellation and async in JS is at least just as (or more) complex than in Rust.
By the way, multithreading has little to do with Pin. I presume you're thinking of Send bounds.
"To work at all" is very dismissive. Those wrappers are complex, but very well abstracted, well defined, and robust, the complexity is essential. Again, look at [1], JS async is hardly less complex, but also much more vague and ill-defined.