Bump example to Expo 52 (#3317)

## Description

This PR fixes some issues that occur when trying to use `RNGH` with
`expo sdk 52`.

This bump will help with testing the [new expo
features](https://docs.expo.dev/guides/tree-shaking/#recursive-optimizations)
and [new react native
features](https://reactnative.dev/docs/react-native-devtools) which will
be useful for optimising Gesture Handler.


## Test plan

<!--
Describe how did you test this change here.
-->

example/app.config.js

@@ -5,7 +5,6 @@ export default ({ config }) => ({
   version: '0.0.1',
   orientation: 'portrait',
   icon: './assets/icon.png',
-  sdkVersion: '51.0.0',
   splash: {
     image: './assets/splash.png',
     resizeMode: 'cover',
@@ -44,16 +43,6 @@ export default ({ config }) => ({
         ],
       },
     ],
-    [
-      'expo-build-properties',
-      {
-        ios: {
-          newArchEnabled: Boolean(Number(process.env.FABRIC_ENABLED)),
-        },
-        android: {
-          newArchEnabled: Boolean(Number(process.env.FABRIC_ENABLED)),
-        },
-      },
-    ],
   ],
+  newArchEnabled: Boolean(Number(process.env.FABRIC_ENABLED)),
 });

example/package.json

@@ -14,31 +14,30 @@
     "postinstall": "patch-package && expo prebuild"
   },
   "dependencies": {
-    "@expo/metro-config": "~0.18.11",
-    "@expo/metro-runtime": "~3.2.3",
-    "@react-native-async-storage/async-storage": "^1.23.1",
-    "@react-native-community/slider": "^4.5.2",
+    "@expo/metro-config": "~0.19.0",
+    "@expo/metro-runtime": "~4.0.1",
+    "@react-native-async-storage/async-storage": "1.23.1",
+    "@react-native-community/slider": "4.5.5",
     "@react-native-community/viewpager": "^5.0.11",
-    "@react-native-masked-view/masked-view": "0.3.1",
+    "@react-native-masked-view/masked-view": "0.3.2",
     "@react-navigation/elements": "^1.3.7",
     "@react-navigation/native": "^6.1.17",
     "@react-navigation/stack": "^6.3.29",
     "@swmansion/icons": "^0.0.1",
-    "expo": "~51.0.38",
-    "expo-build-properties": "^0.12.5",
-    "expo-camera": "~15.0.16",
-    "expo-font": "~12.0.10",
+    "expo": "^52.0.27",
+    "expo-camera": "~16.0.14",
+    "expo-font": "~13.0.3",
     "hoist-non-react-statics": "^3.3.2",
     "invariant": "^2.2.4",
     "patch-package": "^6.5.1",
     "postinstall-postinstall": "^2.1.0",
-    "react": "18.2.0",
-    "react-dom": "18.2.0",
-    "react-native": "0.75.4",
+    "react": "18.3.1",
+    "react-dom": "18.3.1",
+    "react-native": "0.76.6",
     "react-native-gesture-handler": "link:..",
-    "react-native-reanimated": "3.15.5",
-    "react-native-safe-area-context": "4.10.5",
-    "react-native-screens": "3.35.0",
+    "react-native-reanimated": "~3.16.1",
+    "react-native-safe-area-context": "4.12.0",
+    "react-native-screens": "~4.4.0",
     "react-native-svg": "15.8.0",
     "react-native-web": "~0.19.10"
   },
@@ -49,8 +48,7 @@
     "@tsconfig/react-native": "^3.0.5",
     "@types/jest": "^29.5.12",
     "@types/metro-config": "^0.76.3",
-    "@types/react": "~18.2.79",
-    "@types/react-native": "^0.73.0",
+    "@types/react": "~18.3.12",
     "@types/react-test-renderer": "^18.3.0",
     "@typescript-eslint/parser": "^7.8.0",
     "babel-jest": "^29.7.0",