- Extend event handling to include `MouseEvent` and expose it via a new `Event::Mouse` variant.
- Introduce `LayoutSnapshot` to capture the geometry of UI panels each render cycle.
- Store the latest layout snapshot in `ChatApp` for mouse region lookup.
- Implement mouse click and scroll handling across panels (file tree, thinking, actions, code, model info, chat, input, etc.).
- Add utility functions for region detection, cursor placement from mouse position, and scrolling logic.
- Update UI rendering to populate the layout snapshot with panel rectangles.