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/tsconfig.json

@@ -0,0 +1,10 @@
+{
+  "extends": "expo/tsconfig.base",
+  "compilerOptions": {
+    "strict": true,
+    "paths": {
+      "@/*": ["./*"]
+    }
+  },
+  "include": ["**/*.ts", "**/*.tsx", ".expo/types/**/*.ts", "expo-env.d.ts"]
+}