I think the benefit of rust here is that it's not hosted whereas typescript is

The benefit of Rust over TypeScript is that Rust is faster.

TypeScript is memory-safe, but you can't really control where the memory comes from. In Rust you have structs, traits, references and all sorts of things to control both your memory usage and your memory efficiency, and you just don't really get that in TypeScript. Plus, in Rust it's a lot easier to utilize multithreading -- JS is notoriously tedious to parallelize (message-passing between JS workers is a bit annoying compared to structured concurrency in Rust)