@rwudernitz
the problem because of we suddenly upgrade GuzzleHttp to a newer version that dropped support for 5.4 ??
Sorry, but we currently try to fix it and going to release the new fixed version as soon as possible, really sorry for any problem happens to you ??
For a temporary fix,Please login to FTP and then delete the backwpup folder at your wp-content/plugins, after that, you can install the older version of BWP from the zip file in here: https://downloads.www.ads-software.com/plugin/backwpup.3.4.5.zip
Or better, tell your hoster to upgrade PHP version to 5.6 or 7.0.
Sorry again for all the troubles you got ??