While I love Rust, I don't think this here is a good use case for it - TypeScript nowadays works really well with JSX and can be introduced incrementally.
Rust's guarantees work best in a highly concurrent setting - a web app isn't really one.
Rust shines not on the application level, but on the framework/library level, where things like memory usage and performance are critical.
A framework with virtual DOM written entirely in Rust would go a long way. Same with a template compiler.
Both virtual dom and template compilers exist in Rust:
Yew for instance uses both to provide a React-like experience: https://github.com/yewstack/yew
JSX is easy to implement in Rust due to the fact that macros are first class citizen in Rust.