refactor(App, navigation): migrate to Expo Router and clean up navigation structure

- Updated App entry point to utilize Expo Router, simplifying the navigation setup.
- Removed legacy navigation components and services to streamline the codebase.
- Adjusted package.json to reflect the new entry point and updated dependencies for compatibility.
- Enhanced overall application structure by consolidating navigation logic and improving maintainability.

package.json

@@ -1,7 +1,7 @@
 {
   "name": "carrot_bbs",
   "version": "1.0.1",
-  "main": "index.ts",
+  "main": "expo-router/entry",
   "scripts": {
     "start": "expo start",
     "android": "expo run:android",
@@ -25,7 +25,8 @@
     "axios": "^1.13.6",
     "date-fns": "^4.1.0",
     "expo": "~55.0.4",
-    "expo-background-fetch": "~55.0.9",
+    "expo-background-fetch": "~55.0.10",
+    "expo-background-task": "~55.0.10",
     "expo-camera": "^55.0.10",
     "expo-constants": "~55.0.7",
     "expo-dev-client": "~55.0.10",