fix: Update embedding dimensions to 3072 and add Vercel Analytics

- Updated GOOGLE_EMBEDDING_DIMENSIONS to 3072 to match gemini-embedding-001 output
- Updated database schema embedding index from 768 to 3072 dimensions
- Recreated production database index with correct dimensions
- Added @vercel/analytics package for production analytics
- Added Analytics component to root layout

This fixes the galaxy visualization issue caused by dimension mismatch between
the embedding model output (3072) and the database index (768).

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

pnpm-lock.yaml

@@ -47,6 +47,9 @@ importers:
       '@tabler/icons-react':
         specifier: ^3.35.0
         version: 3.35.0(react@19.2.0)
+      '@vercel/analytics':
+        specifier: ^1.5.0
+        version: 1.5.0(next@16.0.1(@babel/core@7.28.5)(@opentelemetry/api@1.9.0)(@playwright/test@1.56.1)(react-dom@19.2.0(react@19.2.0))(react@19.2.0))(react@19.2.0)
       '@xstate/react':
         specifier: ^6.0.0
         version: 6.0.0(@types/react@19.2.2)(react@19.2.0)(xstate@5.24.0)
@@ -1295,6 +1298,32 @@ packages:
     peerDependencies:
       react: '>= 16.8.0'
 
+  '@vercel/analytics@1.5.0':
+    resolution: {integrity: sha512-MYsBzfPki4gthY5HnYN7jgInhAZ7Ac1cYDoRWFomwGHWEX7odTEzbtg9kf/QSo7XEsEAqlQugA6gJ2WS2DEa3g==}
+    peerDependencies:
+      '@remix-run/react': ^2
+      '@sveltejs/kit': ^1 || ^2
+      next: '>= 13'
+      react: ^18 || ^19 || ^19.0.0-rc
+      svelte: '>= 4'
+      vue: ^3
+      vue-router: ^4
+    peerDependenciesMeta:
+      '@remix-run/react':
+        optional: true
+      '@sveltejs/kit':
+        optional: true
+      next:
+        optional: true
+      react:
+        optional: true
+      svelte:
+        optional: true
+      vue:
+        optional: true
+      vue-router:
+        optional: true
+
   '@vercel/oidc@3.0.3':
     resolution: {integrity: sha512-yNEQvPcVrK9sIe637+I0jD6leluPxzwJKx/Haw6F4H77CdDsszUn5V3o96LPziXkSNE2B83+Z3mjqGKBK/R6Gg==}
     engines: {node: '>= 20'}
@@ -4591,6 +4620,11 @@ snapshots:
       '@use-gesture/core': 10.3.1
       react: 19.2.0
 
+  '@vercel/analytics@1.5.0(next@16.0.1(@babel/core@7.28.5)(@opentelemetry/api@1.9.0)(@playwright/test@1.56.1)(react-dom@19.2.0(react@19.2.0))(react@19.2.0))(react@19.2.0)':
+    optionalDependencies:
+      next: 16.0.1(@babel/core@7.28.5)(@opentelemetry/api@1.9.0)(@playwright/test@1.56.1)(react-dom@19.2.0(react@19.2.0))(react@19.2.0)
+      react: 19.2.0
+
   '@vercel/oidc@3.0.3': {}
 
   '@webgpu/types@0.1.66': {}