Adopt UISearchTab for role="search" on iOS 26+ to enable automatic search activation

[cookshelf-katie]

On iOS 26, <NativeTabs.Trigger role="search"> (via expo-router) renders with the new search-tab visual treatment — separated pill, docked field — but does not auto-focus the search field or open the keyboard when the tab is tapped. Apple's own apps (App Store, Maps) do.

This is not about displaying the search tab chrome; that already works. The missing behavior is automatic activation of the attached UISearchController when selecting the search tab, which appears to require UISearchTab rather than UITabBarItem(systemItem: .search).

The native iOS 26 API for this is UISearchTab.automaticallyActivatesSearch. From the docs: "the search field activates automatically upon tab selection, provided the view controller's navigationItem has a non-nil searchController."

Why we don't get it for free today

RCTConvert+RNSBottomTabs.mm:74 maps 'search' to RNSBottomTabsScreenSystemItemSearch, and RNSConversions-BottomTabs.mm:356 converts that to UITabBarSystemItemSearch. iOS 26 dresses up the legacy system item with the new chrome automatically, which is why the visual is right. But the auto-activation behavior is gated on actually using the new UISearchTab class, which we never instantiate.

Repro

Set up a search tab per the expo-router native tabs docs with a Stack.SearchBar inside, run on iOS 26, tap the search tab from another tab.

• Expected: keyboard opens, field is focused.
• Actual: tab is visible, field is empty, no keyboard. User must tap the field.

Proposal

When role="search" on iOS 26+, use UISearchTab with automaticallyActivatesSearch = true instead of UITabBarItem(systemItem: .search). Optionally expose automaticallyActivatesSearch as a prop so consumers can opt out.

Versions: react-native-screens ~4.23.0, react-native 0.83.6, expo ~55.0.9, iPhone 17 Pro on iOS 26.2.