It would be easy and potentially useful for others if there was a Action set up to automatically build the project into a binary that can just be downloaded and ran independently

There are a bunch of packages to do this and it can be done simply in perhaps one line like the following:

pyinstaller -F program.py

Other common packages to look into for this are py2exe and Cython.

Actions like this are commonly available like this one
https://github.com/marketplace/actions/pyinstaller-action