The hardest part would probably be getting LLVM (written in C++) to compile to webassembly, since that's what rust uses as a compiler backend.
https://github.com/jprendes/emception (2021)
https://github.com/tbfleming/cib (2017)
https://github.com/kripken/llvm.js (2012)
I agree it would be great to see this repl running 100% in the browser!