Simplify to just use environment variables

- Remove unnecessary Lambda function and API route
- Remove backend deployment from amplify.yml
- Just use process.env.YOUTUBE_API_KEY directly
- Keep it simple - no need for complex secret management

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

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

amplify/backend.ts

@@ -1,7 +1,6 @@
 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
@@ -9,5 +8,4 @@ import { youtubeApi } from './functions/youtube-api/resource';
 defineBackend({
   auth,
   data,
-  youtubeApi,
 });