Update package.json to make the dist avaliable again (#23991)

### Description
Adding back missing dist folder




### Motivation and Context
<!-- - Why is this change required? What problem does it solve?
- If it fixes an open issue, please link to the issue here. -->

Author: jchen351

js/react_native/e2e/src/App.tsx

@@ -44,7 +44,7 @@ export default class App extends React.PureComponent<{}, State> {
         // test creating session with path
         console.log('Creating with path');
         const pathSession: InferenceSession = await InferenceSession.create(modelPath);
-        pathSession.release();
+        void pathSession.release();
 
         // and with bytes
         console.log('Creating with bytes');