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/hooks/useEmotions.ts

@@ -0,0 +1,13 @@
+import { useQuery } from '@tanstack/react-query';
+import api from '@/lib/api';
+import type { Emotion } from '@/types';
+
+export function useEmotions() {
+  return useQuery<Emotion[]>({
+    queryKey: ['emotions'],
+    queryFn: async () => {
+      const response = await api.get('/emotions');
+      return response.data;
+    },
+  });
+}