Yes, currently input goes into a propmpt() and it doesn't output anything unless you hit "Cancel" on the prompt, definitely a bad time.

Python allows you to reach in and replace the core interpreter loop, so this may be an avenue to have our own asyncify-like function pop out to JS land and restore state correctly (which we can be smart about since we are the interpreter).

It may also be possible to write something that runs Python in a webworker and communicate with it over a sharedarraybuffer, but that I'm a bit more hazy on. Pyodide has some discussion of this in https://github.com/pyodide/pyodide/issues/1219 and https://github.com/pyodide/pyodide/issues/1503.

This is definitely the hardest part of getting Python to work. Well, hardest after the hardest part of building a compiler toolchain like Emscripten :)