fix(mobile): Stabilize native stack option updates

[juliusmarminge]

Extracted from #3910.

Avoids redundant native-stack setOptions updates during busy thread renders, preventing the PreventRemoveProvider maximum-update-depth failure. Includes the matching patched-dependency lockfile update.

Validation inherited from #3910: vp check and mobile native lint passed before the split. The full typecheck is currently blocked in this workspace by unavailable mobile dependencies (expo-blur, expo-quick-actions, and @tabler/icons-react-native).

Note

Stabilize native stack option updates to prevent redundant navigation.setOptions calls

• Adds optionsSignature to produce a stable string fingerprint of an options object, handling primitives, functions (via source), arrays, and objects with cycle detection and stable key ordering.
• Adds stabilizeOptionFunctions to replace function-valued options with stable wrapper references that always delegate to the latest implementation, preventing reference churn on re-renders.
• In NativeStackScreenOptions, computes a signature of the stable options on each render and skips calling navigation.setOptions if the signature matches the previously applied one.
• Behavioral Change: navigation.setOptions is now a no-op when options are semantically unchanged; function options are passed as persistent wrapper references rather than new closures each render.

^{Macroscope summarized f3d9691.}

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Note

Medium Risk
Changes navigation header update timing for all native-stack screens; incorrect signature or wrapper logic could leave stale headers or miss legitimate option updates.

Overview
Stops redundant navigation.setOptions on busy thread screens by treating semantically equal header options as unchanged, addressing PreventRemoveProvider maximum-update-depth failures during re-renders.

NativeStackScreenOptions now builds stable option objects via stabilizeOptionFunctions (stable wrapper identities for inline header factories while still calling the latest closures) and compares an optionsSignature (deep structural hash with function source text and refs ignored) before applying. setOptions runs only when that signature changes, not on every layout pass from fresh object literals.

The @react-navigation/native-stack patch lockfile hash is updated to match the current patched dependency artifact.

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