There is a previous thread wrt how far rustc is to being able to be compiled to WebAssembly, however, the thread hasn't really stated a current state.
I was thinking recently about an in-browser playground equivalent, one that runs in WASM, compiles to WASM, and then runs the compiled WASM directly on the browser.
Aside from the problem of sandboxing another WASM process like that (monitoring it, and also cutting it off if it runs too long), I find the idea of rustc.wasm pretty tantalizing, I see some reddit discussion (1, 2), but no concrete status or pointers.