Configure Amplify Gen 2 backend with secrets

- Add secret definition to backend.ts using proper Amplify Gen 2 syntax
- Update amplify.yml to include backend build phase
- This should properly expose secrets as environment variables

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

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

amplify/backend.ts

@@ -1,11 +1,18 @@
-import { defineBackend } from '@aws-amplify/backend';
+import { defineBackend, secret } from '@aws-amplify/backend';
 import { auth } from './auth/resource';
 import { data } from './data/resource';
 
 /**
  * @see https://docs.amplify.aws/react/build-a-backend/ to add storage, functions, and more
  */
-defineBackend({
+const backend = defineBackend({
   auth,
   data,
 });
+
+// Define secrets that will be available as environment variables
+backend.addOutput({
+  custom: {
+    YOUTUBE_API_KEY: secret('YOUTUBE_API_KEY'),
+  },
+});