[pigeon] Clean up legacy registrant code

[stuartmorgan-g]

Now that the new APIs are available on stable, remove the view controller subclass workaround and use the standard scene-friendly registration system for channel code.

[flutter-dashboard]

It looks like this pull request may not have tests. Please make sure to add tests or get an explicit test exemption before merging.

If you are not sure if you need tests, consider this rule of thumb: the purpose of a test is to make sure someone doesn't accidentally revert the fix. Ask yourself, is there anything in your PR that you feel it is important we not accidentally revert back to how it was before your fix?

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[stuartmorgan-g]

You'll want to apply these changes to your new example copy in your PR.

[gemini-code-assist]

Code Review

This pull request updates the iOS runner example in Pigeon to adopt FlutterImplicitEngineDelegate on AppDelegate instead of using a custom ExampleViewController subclass. It also updates the storyboard to use FlutterViewController directly. The review feedback points out an unused controller variable in AppDelegate.swift that can be safely removed.