fix(iOS): flickering custom header items (software-mansion#2247)

## Description

This PR intents to fix flickering custom header items when going to a
previous screen on `fabric` architecture.
The items are unmounted before the transition happens when `POP` action
is dispatched on navigation from JS causing the items to vanish for a
moment.
The adopted solution uses snapshots of the custom items to be used until
the transition's done.

Fixes software-mansion#2243.

## Changes

- added snapshots of the custom header items
- modified `Test556` for repro

## Screenshots / GIFs

### Before


https://github.com/user-attachments/assets/9da060ed-b65e-4b32-9ab1-debfc2bfd02d


### After


https://github.com/user-attachments/assets/0413fab0-05f6-4e55-adab-f283e01bc551


## Test code and steps to reproduce

- Use `Test556` repro

## Checklist

- [x] Ensured that CI passes

---------

Co-authored-by: Kacper Kafara <kacperkafara@gmail.com>

apps/src/tests/Test556.tsx

@@ -0,0 +1,70 @@
+import * as React from 'react';
+import { Button, StyleSheet, Text, View } from 'react-native';
+import { NavigationContainer, ParamListBase } from '@react-navigation/native';
+import { NativeStackNavigationProp, createNativeStackNavigator } from '@react-navigation/native-stack';
+
+const Stack = createNativeStackNavigator();
+
+type ScreenBaseProps = {
+  navigation: NativeStackNavigationProp<ParamListBase>;
+}
+
+export default function App() {
+  return (
+    <NavigationContainer>
+      <Stack.Navigator
+        screenOptions={{
+          animation: 'fade',
+        }}>
+        <Stack.Screen name="First" component={First} options={{
+          headerTitle: () => (
+            <View style={[styles.container, { backgroundColor: 'goldenrod' }]}>
+              <Text>Hello there!</Text>
+            </View>
+          ),
+          headerRight: () => (
+            <View style={[styles.container, { backgroundColor: 'lightblue' }]}>
+              <Text>Right-1</Text>
+            </View>
+          ),
+        }} />
+        <Stack.Screen name="Second" component={Second} options={{
+          headerTitle: () => (
+            <View style={[styles.container, { backgroundColor: 'mediumseagreen' }]}>
+              <Text>General Kenobi</Text>
+            </View>
+          ),
+          headerRight: () => (
+            <View style={[styles.container, { backgroundColor: 'mediumvioletred' }]}>
+              <Text>Right-2</Text>
+            </View>
+          ),
+        }} />
+      </Stack.Navigator>
+    </NavigationContainer>
+  );
+}
+
+function First({ navigation }: ScreenBaseProps) {
+  return (
+    <Button
+      title="Tap me for second screen"
+      onPress={() => navigation.navigate('Second')}
+    />
+  );
+}
+
+function Second({ navigation }: ScreenBaseProps) {
+  return (
+    <Button
+      title="Tap me for first screen"
+      onPress={() => navigation.popTo('First')}
+    />
+  );
+}
+
+const styles = StyleSheet.create({
+  container: {
+    padding: 3,
+  },
+});

ios/RNSScreenStackHeaderConfig.mm

@@ -628,6 +628,8 @@ + (void)updateViewController:(UIViewController *)vc
   navitem.titleView = nil;
 
   for (RNSScreenStackHeaderSubview *subview in config.reactSubviews) {
+    // This code should be kept in sync on Fabric with analogous switch statement in
+    // `- [RNSScreenStackHeaderConfig replaceNavigationBarViewsWithSnapshotOfSubview:]` method.
     switch (subview.type) {
       case RNSScreenStackHeaderSubviewTypeLeft: {
 #if !TARGET_OS_TV
@@ -755,10 +757,39 @@ - (void)mountChildComponentView:(UIView<RCTComponentViewProtocol> *)childCompone
 
 - (void)unmountChildComponentView:(UIView<RCTComponentViewProtocol> *)childComponentView index:(NSInteger)index
 {
+  // For explanation of why we can make a snapshot here despite the fact that our children are already
+  // unmounted see https://github.com/software-mansion/react-native-screens/pull/2261
+  [self replaceNavigationBarViewsWithSnapshotOfSubview:(RNSScreenStackHeaderSubview *)childComponentView];
   [_reactSubviews removeObject:(RNSScreenStackHeaderSubview *)childComponentView];
   [childComponentView removeFromSuperview];
 }
 
+- (void)replaceNavigationBarViewsWithSnapshotOfSubview:(RNSScreenStackHeaderSubview *)childComponentView
+{
+  UINavigationItem *navitem = _screenView.controller.navigationItem;
+  UIView *snapshot = [childComponentView snapshotViewAfterScreenUpdates:NO];
+
+  // This code should be kept in sync with analogous switch statement in
+  // `+ [RNSScreenStackHeaderConfig updateViewController: withConfig: animated:]` method.
+  switch (childComponentView.type) {
+    case RNSScreenStackHeaderSubviewTypeLeft:
+      navitem.leftBarButtonItem.customView = snapshot;
+      break;
+    case RNSScreenStackHeaderSubviewTypeCenter:
+    case RNSScreenStackHeaderSubviewTypeTitle:
+      navitem.titleView = snapshot;
+      break;
+    case RNSScreenStackHeaderSubviewTypeRight:
+      navitem.rightBarButtonItem.customView = snapshot;
+      break;
+    case RNSScreenStackHeaderSubviewTypeSearchBar:
+    case RNSScreenStackHeaderSubviewTypeBackButton:
+      break;
+    default:
+      RCTLogError(@"[RNScreens] Unhandled subview type: %ld", childComponentView.type);
+  }
+}
+
 static RCTResizeMode resizeModeFromCppEquiv(react::ImageResizeMode resizeMode)
 {
   switch (resizeMode) {