chore: update example app on how to embed SwiftUI auth in UIKit

[russellwheatley]

• Updated example app to demonstrate how to embed FirebaseUI Swift into UIKit app.

[gemini-code-assist]

Summary of Changes

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This pull request introduces a valuable example to the sample application, illustrating how to effectively integrate SwiftUI-based Firebase authentication flows into existing UIKit view hierarchies. This enhancement provides developers with a flexible approach to leverage modern SwiftUI authentication components while maintaining their established UIKit application structure, facilitating a smoother transition and adoption of new frameworks.

Highlights

• New Example Added: A new example demonstrating how to embed FirebaseSwiftUI authentication within a UIKit application has been added.
• UIKit Integration: The example utilizes UIViewControllerRepresentable to host a SwiftUI AuthPickerView inside a UIKit UIViewController, showcasing seamless integration.
• Authentication Flow Demonstration: The new example includes UI elements and logic to clearly illustrate both unauthenticated and authenticated states within the embedded view.

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[gemini-code-assist]

Code Review

This pull request adds a helpful example demonstrating how to embed Firebase's SwiftUI authentication views within a UIKit application. The implementation is generally well-structured, using UIViewControllerRepresentable to bridge between SwiftUI and UIKit. I've identified a couple of areas for improvement to enhance the clarity and correctness of the example code. Specifically, I've suggested simplifying the makeUIViewController method and refining the logic for presenting the authentication sheet to provide a more intuitive user experience. Overall, this is a valuable addition to the sample app.