To ensure efficient backup Storage of your website content, follow these steps:

• Log in to your old MAGIX or Xara web space using an FTP program.

MAGIX Online World: ftp.magix-online.com 

Xara Hosting: sftp.xara-online.com

• Enter the username and password associated with your hosting account. 
• Once connected, navigate to the web folder or root directory of your website and download the complete content of your folder. Please refer to the documentation of your chosen FTP client for detailed instructions on how to download files from a server.
• After successfully downloading the content, connect to the new FTP server and upload your website on the new host. 

If your projects were created using MAGIX Web Designer, Web Designer Premium, or Xara Designer Pro and you still have the project files (*.web), instead of manually downloading and uploading the website content, you can simply republish your website on the new web space using the respective program. 
Here is a short guide for you:
https://www.magix.info/us/support/article/how-to-change-your-ftp-settings--406/

For additional details refer to the support documents for your new hosting provider.