From the paper:

Regarding web workers, \jshelter{} emulates them in the main
thread (inheriting the wrapped JavaScript environment) by default.
The NSCL provides another option: wrapping
workers by injecting the wrappers in their own browser context via its
\verb|patchWorkers()| API. The implementation is very complex and still
experimental\footnote{\url{https://github.com/hackademix/nscl/blob/20220330/content/patchWorkers.js}}
\footnote{\url{https://github.com/hackademix/nscl/blob/20220330/service/patchWorkers.js}}.
It needs more testing before it can be confidently deployed to a general audience.

This issue should track progress regarding the NSCL support for patching web sorkers.