I tried this a few years ago with a Gameboy emulator I had ported from Go to webassembly and used web workers to run the emulator in.
Getting the keyboard input in, in a performant way was a real struggle using postMessage, although I'll admit I'm not the best at web programming so someone more skilled might have been able to do it better
How is keyboard input different from any other sort of data round trip to/from a web worker?
It's the same as when you make a python UI all in one thread, you can't receive user input and also do some long task at the same time.
The emulator ran in the worker, and the inputs were handled on the main thread.
The output (i.e. display) was pushed from the worker -> main thread
I think if I was to do it from scratch I'd do something similar to the DooM approach here and use renderAnimationFrame etc
If you're interested I wrote about it a few years ago but haven't touch it since https://djharper.dev/post/2018/09/21/i-ported-my-gameboy-col...