fix(android): restore image picker after Activity recreation (#7546)

Backport expo/expo#49634 to SDK 54 so retained launchers register
against the current Activity after their previous owner is destroyed.
Cover repeated recreation and replacement-before-destroy ordering with
native regression tests, and document the native rebuild requirement.

Co-authored-by: luke <luopeihuan@gmail.com>
Co-authored-by: Ido Yana <idoyana@gmail.com>
Co-authored-by: RoundRedDot <roundreddot@gmail.com>
Co-authored-by: paseo-bot[bot] <266920839+paseo-bot[bot]@users.noreply.github.com>

scripts/postinstall-patches.mjs

@@ -8,6 +8,12 @@ import { join, relative } from "node:path";
 // workspace root live in their workspace's own node_modules, and patch-package resolves
 // the patch's node_modules/... paths relative to its working directory.
 const patchedPackages = [
+  // Backport for expo-modules-core 57.0.23: https://github.com/expo/expo/pull/49634.
+  // Remove when the installed Expo SDK includes the Activity recreation fix.
+  {
+    nodeModulesPath: "node_modules/expo-modules-core",
+    patchPrefix: "expo-modules-core+",
+  },
   {
     nodeModulesPath: "packages/app/node_modules/react-native-enriched-markdown",
     patchPrefix: "react-native-enriched-markdown+",