If you want to backup a website hosted at Bluehost to upload it to your hosting plan at Hostinger, follow these steps:
Log in to your Bluehost control panel.
Navigate to Advanced → File Manager.
Click on the Site Backup and Restore menu.
Navigate to the public_html folder of your domain, select the files, right-click, and select Compress.
Now you can then download the backup by right-clicking on it and selecting Download.
Additional Resources
Here's a full guide on how to migrate from Bluehost to Hostinger: How to Cancel a Bluehost Account and Migrate Your Services to Another Platform
You can check the guide from Bluehost here: How to Create a Manual Backup of Your Website
If you need further help, make sure to contact Bluehost support