For the moment, the way paper.js supports web worker is by means of exportJSON() and importJSON() methods, which are actually quite time consuming. I was trying to find a way to let paper.js render on OffscreenCanvas directly inside a web worker, and I've managed to do just that. Here's my repo to demonstrate how it works.
https://github.com/MuTsunTsai/paper-worker-test
In those browsers where OffscreenCanvas is not supported, it also has a fallback which is still a lot more efficient than exportJSON() and importJSON(). See README of the repo for more details.
Enjoy!