chore: update the `vite` Asgardeo React boilerplate to use the new SDK

### Current Limitation

The current [`vite` Asgardeo React boilerplate](https://github.com/asgardeo/asgardeo-vite-react-template) uses the soon to be deprecated `@asgardeo/auth-react` SDK.

### Suggested Improvement

Update the [`vite` Asgardeo React boilerplate](https://github.com/asgardeo/asgardeo-vite-react-template) to use the new SDK.

### Please select the package issue is related to

@asgardeo/express, @asgardeo/react

### Version

latest

### Reporter Checklist

- [x] I have searched the existing issues and this is not a duplicate.
- [x] I have provided all the necessary information.
- [x] I have verified the improvement is not available in the latest version of the package.