chore: update dependencies and add AWS Amplify packages

- Added aws-amplify and related packages to dependencies.
- Updated TypeScript and added tsx to devDependencies.
- Modified gallery page to log the availability of the YouTube API key.

amplify/backend.ts

@@ -0,0 +1,11 @@
+import { defineBackend } 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({
+  auth,
+  data,
+});