[feat global_unity_controller] Update examples to null safety

[timbotimbo]

Note

This is the same change as #732, but based on the global_unity_controller feature branch #733 as requested.
In that branch only api_screen.dart was already updated for the new API changes, so the other pages might still be outdated.

Description

The example code can't simply be pasted into a modern flutter project. It will show errors, mainly due to null-safety changes.
Given that the plugin supports null-safety from version 4.2.0 (18 months ago), it's safe to update the example.

The last commit is a small cleanup by following most suggestions of flutter_lints.

Type of Change

• ✨ New feature (non-breaking change which adds functionality)
• 🛠️ Bug fix (non-breaking change which fixes an issue)
• ❌ Breaking change (fix or feature that would cause existing functionality to change)
• 🧹 Code refactor
• ✅ Build configuration change
• 📝 Documentation
• 🗑️ Chore