Implement proper Amplify Gen 2 secret management

- Create Lambda function with secret environment variable
- Add YouTube API function to backend configuration
- Create Next.js API route to handle YouTube requests
- Update gallery page to use API route
- This follows the correct Amplify Gen 2 pattern for secrets

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

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

amplify/backend.ts

@@ -1,6 +1,7 @@
 import { defineBackend } from '@aws-amplify/backend';
 import { auth } from './auth/resource';
 import { data } from './data/resource';
+import { youtubeApi } from './functions/youtube-api/resource';
 
 /**
  * @see https://docs.amplify.aws/react/build-a-backend/ to add storage, functions, and more
@@ -8,4 +9,5 @@ import { data } from './data/resource';
 defineBackend({
   auth,
   data,
+  youtubeApi,
 });