fix(authentication): fixed the authentication loop.

[krishna9358]

Summary

• When using Clerk authentication, the sign-in dialog was triggered automatically via useEffect when the user wasn't authenticated. If the user closed the dialog without signing in, the useEffect wouldn't re-run because none of its dependencies changed. This left users stuck on the "Authentication Required" screen with "Opening sign-in dialog..." but the dialog would never reopen.

Testing

• bun run test
• bun run lint
• bun run typecheck
• Additional notes:

Documentation

• Updated the relevant doc(s) (see docs/guide.md) or checked that no updates are needed.
• Recorded contract/architecture changes in both public docs and .ai logs when applicable.

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