This is actually an unresolved data protection issue.
However, as long as you do not permanently store any data on your private device used for business purposes, but restrict yourself to working in the browser, there is no data that could cause problems when backing up to the cloud.
Make sure that encryption is activated for backups. You can find further information at https://www.bsi.bund.de/DE/Themen/Verbraucherinnen-und-Verbraucher/Basisschutz-fuer-Computer-Mobilgeraete/, for example
For mail apps, please note that you must not use any mail apps that store access data in the provider cloud (unfortunately, Outlook apps do this on both Android and iOS). Using the built-in browser to access https://mail.tu-braunschweig.de/ is not critical.
Suitable mail apps are, for example, Apple Mail on iOS and Nine Folders Mail or FairMail on Android.