I'm trying to wrangle my Gnome desktop windows and I would like to automate their placement using Python. What is a good approach for this?
You have 2 options:
If you only need it to work in an X session, then this is relatively easy to do using xdotool (short summary in this SO answer). You can also use it from Python, as explained in another question on SO.
The Wayland protocol does not allow this by default for security reasons. If you want to be able to support both X and Wayland, you'll have to get to the inner working of GNOME Shell by writing an extension (in JS). This extension then either does the moving, or exposes an API to move windows, which you can then call from a Python script.