Until wasm has GC, we're not likely to see much in the way of compile-to-web outside of C, C++, or Rust.
https://github.com/SteveSanderson/Blazor
https://www.youtube.com/watch?v=MiLAE6HMr10
WebAssembly without native GC support is no different that targeting a real hardware CPU. One just has to implement it as well.
As soon as WebAssembly reaches a more mature state, expect the resurgence of plugins and this time around we won't be able to disable them.
Also if you bother to read the meeting minutes from WebAssembly meetings, developers from .NET team are present in such meetings.