[PyCDE] Write CI flow to be run on 'main' to test if a change broke PyCDE. Do not have it report anywhere.

This one may or may not be possible. I would like a CI pipeline which checks whether or not a commit broke pycde (runs the pycde tests). However, I do not want it to be visible to non-PyCDE developers -- we are on the hook for updating PyCDE. That means they shouldn't get notification emails about it and it shouldn't show up in the commit history page under the green check mark.

We can display a build status badge on the PyCDE page. We can set up a notification sent to pycde devs.

The easiest way to accomplish this is probably a scheduled job.

Start by locating the PyCDE tests and determining how they are currently invoked. Define the scheduled CI flow so it checks PyCDE after changes without reporting to non-PyCDE developers, while providing the requested PyCDE status badge or developer notification; completion means the tests run and the visibility constraints are met.

Written by the indexing model from the issue text.