[Auth] Fix Xcode 26.2 build warning

[paulb777]

The old-style weak handling causes a build warning in Xcode 26.2

Weak variable 'weakSelf' was never mutated; consider changing to 'let' constant

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[paulb777]

/gemini review

[gemini-code-assist]

Code Review

This pull request updates the weak-strong dance pattern to use modern Swift syntax ([weak self] capture list and guard let self else { return }). This change is correct, improves code readability and maintainability, and resolves a build warning in newer Xcode versions. I've added one minor suggestion for consistency in a nested closure. Overall, this is a good improvement.