chore: upgrade dependencies and update routing configuration

Author: dohooo

example/app/app/_layout.tsx

@@ -112,7 +112,7 @@ function RootLayoutNav() {
               </XStack>
             )}
             <Stack
-              initialRouteName="/"
+              initialRouteName="index"
               screenOptions={{
                 headerShown: !inDoc && webHeaderShown,
                 contentStyle: {

example/app/package.json

@@ -18,43 +18,43 @@
   "dependencies": {
     "@expo/vector-icons": "^14.0.2",
     "@faker-js/faker": "^9.0.1",
-    "@react-navigation/native": "^6.0.2",
+    "@react-navigation/native": "^7.0.14",
     "@tamagui/config": "^1.111.13",
     "@tamagui/lucide-icons": "^1.111.13",
-    "expo": "~51.0.28",
-    "expo-blur": "~13.0.2",
-    "expo-dev-client": "~4.0.29",
-    "expo-font": "~12.0.10",
-    "expo-haptics": "~13.0.1",
-    "expo-image": "~1.12.15",
-    "expo-linear-gradient": "~13.0.2",
-    "expo-linking": "~6.3.1",
-    "expo-media-library": "~16.0.5",
-    "expo-router": "~3.5.23",
-    "expo-splash-screen": "~0.27.5",
-    "expo-status-bar": "~1.12.1",
-    "expo-system-ui": "~3.0.7",
-    "expo-updates": "~0.25.25",
-    "expo-web-browser": "~13.0.3",
-    "react": "18.2.0",
-    "react-dom": "18.2.0",
-    "react-native": "0.74.5",
-    "react-native-gesture-handler": "~2.16.1",
-    "react-native-reanimated": "~3.10.1",
+    "expo": "52.0.32",
+    "expo-blur": "~14.0.3",
+    "expo-dev-client": "~5.0.12",
+    "expo-font": "~13.0.3",
+    "expo-haptics": "~14.0.1",
+    "expo-image": "~2.0.5",
+    "expo-linear-gradient": "~14.0.2",
+    "expo-linking": "~7.0.5",
+    "expo-media-library": "~17.0.5",
+    "expo-router": "~4.0.17",
+    "expo-splash-screen": "~0.29.21",
+    "expo-status-bar": "~2.0.1",
+    "expo-system-ui": "~4.0.8",
+    "expo-updates": "~0.26.17",
+    "expo-web-browser": "~14.0.2",
+    "react": "18.3.1",
+    "react-dom": "18.3.1",
+    "react-native": "0.76.7",
+    "react-native-gesture-handler": "~2.20.2",
+    "react-native-reanimated": "~3.16.1",
     "react-native-reanimated-carousel": "link:../..",
-    "react-native-safe-area-context": "4.10.5",
-    "react-native-screens": "3.31.1",
-    "react-native-svg": "15.2.0",
-    "react-native-view-shot": "3.8.0",
-    "react-native-web": "~0.19.10",
+    "react-native-safe-area-context": "4.12.0",
+    "react-native-screens": "~4.4.0",
+    "react-native-svg": "15.8.0",
+    "react-native-view-shot": "~4.0.3",
+    "react-native-web": "~0.19.13",
     "tamagui": "^1.111.13"
   },
   "devDependencies": {
     "@babel/core": "^7.20.0",
-    "@types/react": "18.2.0",
+    "@types/react": "~18.3.12",
     "babel-plugin-module-resolver": "^5.0.2",
     "jest": "^29.2.1",
-    "jest-expo": "~51.0.3",
+    "jest-expo": "~52.0.3",
     "metro-react-native-babel-transformer": "^0.77.0",
     "react-native-svg-transformer": "^1.5.0",
     "react-test-renderer": "18.2.0",