feat: add mobile application structure with emotion picker and API integration

- Added favicon and icon assets for the mobile app.
- Implemented EmotionPicker component for selecting emotions with child options.
- Created hooks for fetching emotions, feeds, and rapport data.
- Established API service for handling requests and authentication.
- Integrated Zustand for state management of user authentication.
- Defined color palette for the application.
- Set up TypeScript types for various entities including User, Emotion, and Feed.
- Configured Babel and TypeScript for the mobile project.
- Added package.json with necessary dependencies for Expo and React Native.

mobile/app.json

@@ -0,0 +1,28 @@
+{
+  "expo": {
+    "name": "CESIZen",
+    "slug": "cesizen",
+    "version": "1.0.0",
+    "orientation": "portrait",
+    "icon": "./assets/icon.png",
+    "userInterfaceStyle": "automatic",
+    "newArchEnabled": true,
+    "scheme": "cesizen",
+    "splash": {
+      "backgroundColor": "#fce117",
+      "resizeMode": "contain"
+    },
+    "ios": {
+      "supportsTablet": true,
+      "bundleIdentifier": "com.cesi.cesizen"
+    },
+    "android": {
+      "adaptiveIcon": {
+        "foregroundImage": "./assets/adaptive-icon.png",
+        "backgroundColor": "#fce117"
+      },
+      "package": "com.cesi.cesizen"
+    },
+    "plugins": ["expo-router", "expo-secure-store", "expo-font"]
+  }
+}