feat(router, docs): Improve authentication guide (#24185)

# Why

- fix https://github.com/expo/router/issues/745
- fix https://github.com/expo/router/issues/430
- fix https://github.com/expo/rou

feat(router, docs): Improve authentication guide (#24185)

# Why

- fix https://github.com/expo/router/issues/745
- fix https://github.com/expo/router/issues/430
- fix https://github.com/expo/router/issues/845
- Further resolve https://github.com/expo/router/issues/740
- Partially resolve https://github.com/expo/router/issues/814

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# How

Revise documentation to provide clearer guidance on avoiding navigation
before the navigation has been mounted. While nesting isn't mandatory,
this adjustment aims to assist newcomers who might be encountering
difficulties, making it less likely to encounter issues.

# Test Plan

I've added an e2e test which isn't run continuously, but it makes it
easier for us to quickly validate that the logic here does in fact make
sense.

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Co-authored-by: James Ide <[email protected]>
Co-authored-by: Aman Mittal <[email protected]>

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