Provided a host hasn't disabled it, cPanel makes it easy to download a FULL back-up.
Other partial backups don't capture everything, and aren't as simple to restore at the other end.
If you're unable to download a Full Back-up from cPanel > Backup Wizard, look for a "home directory" backup instead.
(That fall-back type should provide us with enough information to restore your website FILES ONLY and emails.)
If you were only able to download a home directory back-up, you'll need to access phpMyAdmin, and Export each database using "Quick".
Please then upload that to a secure location that you control, such as a Dropbox/OneDrive/iCloud/Google Drive account, and share a secure link to our team.
If you're moving to LEOPARD.host, our preferred method of migrating is you providing our team with login credentials so we can evaluate options and take the best course of action.