feat: complete Week 1 frontend setup (#9 #10 #11 #12)

- Install and configure Tailwind CSS (#9)
- Install Nuxt UI component library (#10)
- Create app layout with header/footer components (#11)
- Implement Supabase client composable (#12)
- Add TypeScript database types
- Create placeholder pages (index, scan, settings)
- Setup responsive navigation with mobile menu
- Configure auth state management

All Week 1 frontend foundation tasks complete.

app/pages/index.vue

@@ -0,0 +1,57 @@
+<template>
+  <div>
+    <div class="flex items-center justify-between mb-6">
+      <h1 class="text-3xl font-bold text-gray-900">Inventory</h1>
+      
+      <div class="flex gap-2">
+        <UButton 
+          to="/scan" 
+          color="primary" 
+          size="lg"
+          icon="i-heroicons-qr-code"
+        >
+          Scan Item
+        </UButton>
+        
+        <UButton 
+          color="white" 
+          size="lg"
+          icon="i-heroicons-plus"
+        >
+          Add Manually
+        </UButton>
+      </div>
+    </div>
+
+    <!-- Empty State -->
+    <UCard v-if="true">
+      <div class="text-center py-12">
+        <UIcon 
+          name="i-heroicons-inbox" 
+          class="w-16 h-16 text-gray-400 mx-auto mb-4"
+        />
+        <h3 class="text-lg font-semibold text-gray-900 mb-2">
+          No items yet
+        </h3>
+        <p class="text-gray-600 mb-6">
+          Start by scanning a barcode or adding an item manually.
+        </p>
+        <UButton 
+          to="/scan" 
+          color="primary"
+          icon="i-heroicons-qr-code"
+        >
+          Scan First Item
+        </UButton>
+      </div>
+    </UCard>
+
+    <!-- TODO: Item list will go here -->
+  </div>
+</template>
+
+<script setup lang="ts">
+definePageMeta({
+  layout: 'default'
+})
+</script>