One of the interesting things about this is all the tooling created around the JWST. Like there is even a downloadable app that you use to plan & book time. Plus all the documentation, etc.
If you mean the APT (Astronomer's Proposal Tool) this tool was originally developed for Hubble Space Telescope proposals, and has been in use since at least least 2008[0]. A year or two ago, I found that parts of it are written in Common Lisp[1].
[0] https://www.stsci.edu/scientific-community/software/astronom...
[1] https://apst.stsci.edu/apt/documents/documentation/apt-proje...
https://github.com/spacetelescope
The Physical Optics Propagation in PYthon (Poppy) has some neat pictures: https://poppy-optics.readthedocs.io/en/latest/
The Cycle 1 documentation, including the now-expired Call for Proposals is here: https://jwst-docs.stsci.edu/jwst-opportunities-and-policies