Modularize more of the code

App.tsx is currently holding all functionality. Pulling parts out will reduce the bloat and help the code be more manageable without stepping on other code for each new feature. The goal of this issue is to start the process of modularization, not perfectly breakout every function possible.

Start by reading App.tsx to map the functionality currently held there and identify reasonable module boundaries. The issue does not name specific functions, files, or tests, so clarify the intended first extraction before changing code. Done means part of the functionality is modularized while existing behavior remains intact.

Written by the indexing model from the issue text.