Right now. WASM has been supported by every browser for a while now, and most webapps are made with WASM. That said, it's not a replacement for Javascript, most people only use it on things that need to be high performance like heavier apps and web games. Nobody really makes websites that rely on WebAssembly instead of JS to my knowledge.
From my understanding, it’s because WASM is pure (deterministic) and needs stateful entry points in order to work. For this reason, a JavaScript bit to interact with it is a requirement at the moment.
JS is slow, but I program Rust and Scala. Every internal app at my company is react based and I spend most my time waiting for that bloated framework to load a simple table. It can take seconds to load a 20 route paginated table from source.
We've got a WebAssembly web-UI at $DAYJOB. Implementation language is Rust, we use the Leptos framework (although other mature frameworks are available for Rust).
Pros:
Same language and similar tooling as in the backend. Most libraries work the same way (obviously excluding libraries that read from the filesystem, for example). This is especially good, if you've got lots of "full stack" devs.
Same model classes as in the backend. If you change a field, the compiler will force you to fix it on both sides. It is compile-time guaranteed that backend and frontend are compatible.
Rust is a nicer language than JS/TS. I find especially Rust's error handling via Result and Option types + pattern-matching works really well for UI stuff. You just hand the Result value over to your rendering stack and that displays either the value or the error. No unset/null variables, no separate error variable, no ternaries.
Having a strict compiler makes it less bad when you're lax on testing, and frontend code is a pain to test.
Cons:
If you've got pure frontend folks, or people who are deep into React or Angular or whatever, those are not going to be as productive.
The JS ecosystem is massive, you just won't find as many component libraries for Rust, which can definitely also reduce productivity.
With me being in a team with few frontend folks, I would definitely opt for it again.
The biggest hole in WASM right now is being able to DO anything really useful in it, natively. The only thing you can do natively right now is use the CPU. Can't manipulate the DOM. Can't access local storage or cookies or networking APIs, etc. You can call out to arbitrary JS code, but that's it.
This is great for some of the big JS libraries that have very CPU-heavy workloads they can optimize in WASM and call to from JS. Like frequently parsing and re-parsing HTML. Or doing game physics calculations.
I haven't heard word one about WHEN any of this will be available. Which is particularly troubling, given how long people have been begging for it.
Of course, none of this stops you from using WASM in the real world, to do quite a lot of things. You're just gonna have to deal with JS interop, still, do do anything really useful.