There is also a push towards Rust on the web side of things too, it would be amazing to have a single language that could be used for both worlds
In reality of course it's a bit more than just compiler support, you'd want easy interop with Javascript and Web APIs and a working debugger. With the Emscripten SDK and Chrome's and VSCode's WASM DWARF support it's looking pretty good now at least for C and C++ (but I assume the WASM DWARF debugging stuff also works for Rust, since it's the same compiler infrastructure underneath).
Leptos, as a popular recent example, suffers from one major issue (that most others suffer from too): the JSX stuff is opaque to Rust Analyzer. Code completion aside, you lose the ability to hover - massively crippling any hope of tracking down how to resolve a type mismatch.
Web Rust also has the impedance mismatch that Rust has for UI. There are several success stories - e.g. Cosmic Desktop, but I'm certain that there's more love than practicality involved.
I think part of the reason is that we are trying to shove in existing patterns - which originate from OOP languages - into Rust. In both semantic and ergonomic terms I have been bitten by trying to OOP in Rust when I was first learning it.
I think that there exists an (as yet unknown) solution to the UI problem. It's just going to look nothing like React (or Elm even).