Addresses two code review findings from previous commits.

Path parsing in internal/doctor/consistency.go

• Handle branch names containing slashes (e.g., feature/new-ui) by joining all path parts beyond index 3
• Previous implementation only accessed parts[3], truncating multi-segment branch names

Dependency injection in internal/version/update.go

• Replace global mutable state with UpdateChecker struct for testability
• Add constructors: NewUpdateChecker() and NewUpdateCheckerWithURL(url)
• Maintain backward compatibility via deprecated ReleaseURL global variable

// New approach - dependency injection
checker := NewUpdateCheckerWithURL(customURL)
updateAvailable, version, url, err := checker.CheckForUpdate(ctx)

// Still works - backward compatible
updateAvailable, version, url, err := CheckForUpdate(ctx)

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