@neil found the fix. Good sleuthing! 
From the command line:
cd /var/discourse
./launcher enter app
rails c
Upload.update_all(secure: false)
This brings the site back up for me. @biyaniyash please give it a shot and let us know how it goes.
The explanation for this is that, on Discourse for Teams, Secure Media Uploads is enabled which requires S3. On the newly restored self-hosted site, secure media is disabled and uploads are stored locally on the server. But any existing uploads from the backup were already marked as secure, resulting in errors.