feat: improve Example App

The Example app currently uses a Drawer(deprecated component) for navigation and a simple list based navigation to go each component showcase.
This could be improved by:
- replacing the drawer with a more modern UI like a modal sheet for global configuration of theme configuration
- adding a search functionality
- a main "sample" section when the user first opens the app showcasing a mix of different components like on https://oss.callstack.com/react-native-paper/ or https://material-foundation.github.io/material-theme-builder/

Start by inspecting the Example app's current Drawer navigation and component showcase list, then review the linked reference apps for possible directions. Done would require an agreed design that replaces the deprecated navigation, adds search, and provides a mixed sample section on first launch.

Written by the indexing model from the issue text.