chore: migrate to using examples folder for RN libraries

[moldy530]

Pull Request Checklist

• Did you add new tests and confirm existing tests pass? (yarn test)
• Did you update relevant docs? (docs are found in the site folder, and guidelines for updating/adding docs can be found in the contribution guide)
• Do your commits follow the Conventional Commits standard?
• Does your PR title also follow the Conventional Commits standard?
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PR-Codex overview

This PR primarily focuses on removing the example directory from the account-kit/rn-signer project and updating files in both react-native-bare-example and react-native-expo-example. It also includes some formatting and dependency updates.

Detailed summary

• Deleted the entire example directory from account-kit/rn-signer.
• Updated the API_KEY in .env.example.
• Modified package.json in react-native-bare-example for dependency versions.
• Adjusted styles and formatting in several components.
• Enhanced error handling in authentication processes.
• Updated babel.config.js and metro.config.js for consistency.
• Improved README documentation for clarity.

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[moldy530]

• chore: migrate to using examples folder for RN libraries #1642 👈 (View in Graphite)
• main

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