docs: correctly use authenticate in docs

[blakecduncan]

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PR-Codex overview

This PR focuses on refactoring authentication handling in various components by changing the authenticate function calls from asynchronous (async/await) to synchronous style, while also adding success and error handling callbacks.

Detailed summary

• Updated MyAuthComponent to include authenticateAsync.
• Changed handleGoogleRedirectLogin, handleGooglePopupLogin, and other login methods to use synchronous authenticate calls.
• Added onSuccess and onError callbacks for better error handling and success feedback.
• Refactored email and passkey related methods to follow the same pattern.

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[dphilipson]

For discussion: do we want to be encouraging the use of authenticateAsync over authenticate? I'd say using authenticate would typically lead to more robust apps, although it does possibly have a bit of knowledge overhead.

[blakecduncan]

For discussion: do we want to be encouraging the use of authenticateAsync over authenticate? I'd say using authenticate would typically lead to more robust apps, although it does possibly have a bit of knowledge overhead.

@dphilipson Yeah that's a good question. I was thinking the async function might be easier to understand for someone not familiar with react query. I think you are right though we should probably recommend the non async one.