Seprate the model from the GUI/rendering code

Currently the code that describes the state of the application (i.e., the model) is heavily intermixed with the code to make the GUI and render the scene. This makes it difficult to serialize/deserialize the current state (e.g., for saving and loading checkpoints) and to swap out the back end if necessary in the future.

No files, tests, or entry points are named. Start by mapping where application state, GUI construction, and scene rendering currently meet, then identify the serialization boundaries needed for saving and loading checkpoints. Done means the model is separated from GUI and rendering code without losing the stated ability to swap the backend.

Written by the indexing model from the issue text.