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/auth/resource.ts

@@ -0,0 +1,11 @@
+import { defineAuth } from '@aws-amplify/backend';
+
+/**
+ * Define and configure your auth resource
+ * @see https://docs.amplify.aws/gen2/build-a-backend/auth
+ */
+export const auth = defineAuth({
+  loginWith: {
+    email: true,
+  },
+});