Update amplify.yml to inject environment variable

- Create .env.production file with YOUTUBE_API_KEY during build
- This ensures Next.js can access the environment variable

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

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

amplify.yml

@@ -6,6 +6,7 @@ frontend:
         - npm ci
     build:
       commands:
+        - echo "YOUTUBE_API_KEY=$YOUTUBE_API_KEY" >> .env.production
         - env | grep YOUTUBE_API_KEY || echo "YOUTUBE_API_KEY not found in environment"
         - npm run build
   artifacts: